100 High-Scoring Electrostatics MCQs: From Basics to Expert Level

⚡ Master Electrostatics with These MCQs – From Basic to Expert Level! ⚡

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👉Physics MCQs Hub – Unit wise Physics MCQs Practice (Main-Page)👈

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Are you preparing for exams or just want to strengthen your understanding of Electrostatics? This post is your ultimate one-stop resource!
We have carefully compiled 100 Multiple-Choice Questions (MCQs) covering every important concept – from basic principles to intermediate applications, and all the way to advanced and expert-level problems. Each question comes with the correct answer and clear explanations, so you don’t just memorize – you understand!

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Here’s what you’ll get:
Set-1: Basic Level – Perfect for beginners, covering fundamentals like Coulomb’s Law, Electric Field, and Potential.
Set-2: Intermediate Level – Challenges your application skills, including Gauss’s Law, Dipoles, and Capacitors.
Set-3: Advanced Level – For deeper understanding and problem-solving, including complex dipole configurations and energy calculations.
Set-4: Expert Level – Tough questions that test conceptual clarity, problem-solving speed, and critical thinking.

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Whether you are a high school student, competitive exam aspirant, or a physics enthusiast, these MCQs will help you:

Strengthen concepts
Practice numerical problems
Prepare efficiently for exams

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💡 Tip: Try solving each question before checking the answer to maximize learning.

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Get ready to boost your Electrostatics skills – from basic charges to complex fields! 

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Electrostatics MCQs (Set-1: Basic Level)

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1. What is the SI unit of electric charge?
a) Volt
b) Coulomb
c) Ampere
d) Newton
Answer: b) Coulomb
Explanation: Electric charge is measured in coulombs (C), defined as 1 ampere × 1 second.

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2. Two point charges attract each other with a force of 9 N in vacuum. If the medium between them is oil with relative permittivity 3, the force becomes:
a) 3 N
b) 9 N
c) 27 N
d) 1 N
Answer: a) 3 N
Explanation: Force in a medium: $F=\frac{F_0}{{ϵ}_r}$. Here, $F_0=9\text{ N},{ϵ}_r=3\Rightarrow F=9\mathrm{/}3=3\text{ N}$.

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3. Coulomb’s law gives the force between:
a) Two magnetic poles
b) Two point charges
c) A current-carrying wire and a magnet
d) Two parallel plates
Answer: b) Two point charges
Explanation: Coulomb’s law applies to the electrostatic force between two stationary point charges.

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4. Electric field at a point is defined as:
a) Force on any charge at that point
b) Force per unit positive charge
c) Potential energy per unit charge
d) Work done on a negative charge
Answer: b) Force per unit positive charge
Explanation: $E=F\mathrm{/}q$, where F is the force experienced by a small positive test charge q.

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5. Electric field due to a point charge is:
a) Inversely proportional to r
b) Inversely proportional to $r^2$ 
c) Proportional to $r^2$ 
d) Independent of distance
Answer: b) Inversely proportional to $r^2$ 
Explanation: $E=\frac{1}{4\pi {ϵ}_0}\frac{q}{r^2}$.

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6. Electric field is a vector quantity because it has:
a) Magnitude only
b) Direction only
c) Both magnitude and direction
d) Neither magnitude nor direction
Answer: c) Both magnitude and direction
Explanation: Electric field has direction along the force on a positive test charge and magnitude $E=F\mathrm{/}q$.

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7. Electric field at the centre of a uniformly charged ring is:
a) Maximum
b) Zero
c) $q\mathrm{/}4\pi {ϵ}_0{r}^2$ 
d) Infinity
Answer: b) Zero
Explanation: Symmetry cancels all contributions; net field at the centre of a ring is zero.

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8. Electric flux through a closed surface depends on:
a) Surface area only
b) Charge enclosed only
c) Shape of the surface
d) Dielectric medium only
Answer: b) Charge enclosed only
Explanation: By Gauss’s law, ${\mathrm{\Phi }}_E=q_{\text{enclosed}}\mathrm{/}{ϵ}_0$.

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9. A positive test charge is placed in an electric field. The direction of the electric field is:
a) Opposite to force on the charge
b) Same as force on the charge
c) Perpendicular to the force
d) None of these
Answer: b) Same as force on the charge
Explanation: Electric field is the force experienced by a positive test charge per unit charge.

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10. Unit of electric flux in SI system is:
a) N·m²/C
b) N/C
c) C/N·m²
d) V/m
Answer: a) N·m²/C
Explanation: Electric flux ${\mathrm{\Phi }}_E=E\cdot A\cos \theta$ ; unit is N·m²/C.

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11. The potential at a point in an electric field is defined as:
a) Work done per unit positive charge
b) Force per unit charge
c) Energy of a negative charge
d) Electric field at that point
Answer: a) Work done per unit positive charge
Explanation: $V=W\mathrm{/}q$, where W is work done to bring q from infinity to that point.

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12. Electric potential is a scalar quantity because it has:
a) Magnitude only
b) Direction only
c) Both magnitude and direction
d) Neither
Answer: a) Magnitude only
Explanation: Potential is independent of direction; it is just the work done per unit charge.

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13. Two equal positive charges are placed at a distance. The point where the electric field is zero lies:
a) Midway between them
b) Closer to the smaller charge
c) Outside the line joining them
d) Anywhere
Answer: b) Closer to the smaller charge
Explanation: Fields oppose; net field is zero closer to the smaller charge (for unequal charges).

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14. Work done in moving a charge along an equipotential surface is:
a) Maximum
b) Minimum
c) Zero
d) Depends on speed
Answer: c) Zero
Explanation: Electric potential is constant on an equipotential; no work is required.

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15. Electric dipole consists of:
a) Two equal positive charges
b) Two equal negative charges
c) Equal and opposite charges separated by a distance
d) Single charge
Answer: c) Equal and opposite charges separated by a distance
Explanation: Dipole moment $\vec{p}=q\cdot \vec{d}$, points from negative to positive.

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16. Electric field due to an infinite uniformly charged plane is:
a) Zero at all points
b) Same at all points
c) Depends on distance
d) Infinity
Answer: b) Same at all points
Explanation: Field is independent of distance: $E=\sigma \mathrm{/}2{ϵ}_0$ .

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17. Electric field inside a hollow spherical conductor is:
a) Zero
b) Maximum at center
c) Same as on surface
d) Depends on radius
Answer: a) Zero
Explanation: By Gauss’s law, no net flux inside a conductor; field is zero.

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18. Electric field near the edge of two large parallel plates:
a) Uniform everywhere
b) Stronger at edges (fringing)
c) Zero at center
d) Infinite
Answer: b) Stronger at edges (fringing)
Explanation: Edge effects cause the field to bulge outward near edges; uniform only in central region.

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19. The potential difference between two points is:
a) Work done on unit positive charge
b) Force on charge
c) Energy per mole of charges
d) Charge per unit energy
Answer: a) Work done on unit positive charge
Explanation: $V=W\mathrm{/}q$, standard definition of electric potential difference.

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20. Electric field and potential are related by:
a) $E=-dV\mathrm{/}dr$ 
b) $E=V^2$ 
c) $V=Ed$ 
d) $E=V\mathrm{/}d$ 
Answer: a) $E=-dV\mathrm{/}dr$ 
Explanation: Electric field is negative gradient of potential.

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21. A proton is placed in a uniform electric field. Its acceleration is:
a) Zero
b) Same as electron in same field
c) Depends on charge
d) Depends on mass
Answer: d) Depends on mass
Explanation: $a=F\mathrm{/}m=qE\mathrm{/}m$. Proton is heavier than electron → smaller acceleration for same field.

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22. The principle of superposition in electrostatics states:
a) Forces due to multiple charges add vectorially
b) Only one charge produces field
c) Force is scalar sum
d) Potential is zero
Answer: a) Forces due to multiple charges add vectorially
Explanation: Net force on a charge is vector sum of forces due to all other charges.

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23. Capacitance is defined as:
a) Charge per unit potential difference
b) Potential difference per unit charge
c) Energy stored per charge
d) Force per unit area
Answer: a) Charge per unit potential difference
Explanation: $C=Q\mathrm{/}V$ .

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24. Electric field at a point due to an electric dipole on its axial line is:
a) Zero
b) Maximum at centre

c) $E=\frac{1}{4\pi {ϵ}_0}\frac{2p}{r^3}$

d) $E=\frac{1}{4\pi {ϵ}_0}\frac{p}{r^2}$
Answer: c) $E=\frac{1}{4\pi {ϵ}_0}\frac{2p}{r^3}$
Explanation: Field on axial line of dipole: $E=\frac{1}{4\pi {ϵ}_0}\frac{2p}{r^3}$, along dipole axis.

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25. The torque on a dipole in a uniform electric field is given by:
a) $\tau =pE\cos \theta$ 
b) $\tau =pE\sin \theta$ 
c) $\tau =p\mathrm{/}E$ 
d) $\tau =E\mathrm{/}p$ 
Answer: b) $\tau =pE\sin \theta$
Explanation: Torque tends to align dipole with field; magnitude $\tau =pE\sin \theta$.

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Electrostatics MCQs (Set-2: Intermediate Level, Q26–50)

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26. Two charges, +3 μC and -2 μC, are 1 m apart. The electric field at midpoint is:
a) 2 × 10⁶ N/C
b) 5 × 10⁶ N/C
c) 0
d) 1 × 10⁶ N/C
Answer: b) 5 × 10⁶ N/C
Explanation: Fields add vectorially: $E=k(\mathrm{\mid }{q}_1\mathrm{\mid }+\mathrm{\mid }{q}_2\mathrm{\mid })\mathrm{/}{r}^2$ at midpoint (considering opposite directions).

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27. Electric field inside a uniformly charged spherical shell:
a) Varies linearly with radius
b) Zero
c) Maximum at center
d) Same as surface
Answer: b) Zero
Explanation: By Gauss’s law, net enclosed charge inside shell = 0 → field = 0.

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28. Work done in moving a charge from infinity to a point near a positive point charge is:
a) Positive
b) Negative
c) Zero
d) Depends on path
Answer: b) Negative
Explanation: Like charges repel; potential energy decreases when a positive charge moves toward another positive charge.

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29. The electric field midway between two equal and opposite charges (dipole) is:
a) Zero
b) Maximum along axial line
c) Maximum along perpendicular bisector
d) Infinity
Answer: b) Maximum along axial line
Explanation: Axial line field: $E=2kp\mathrm{/}{r}^3$; perpendicular bisector: $E=kp\mathrm{/}{r}^3$ .

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30. Electric field between two large parallel plates is:
a) Uniform
b) Stronger near edges
c) Zero inside
d) Depends on plate material
Answer: a) Uniform
Explanation: Central region of large plates → $E=\sigma \mathrm{/}{ϵ}_0$, uniform.

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31. A charge of 5 μC experiences a force of 2 N. The electric field is:
a) 1 × 10⁶ N/C
b) 4 × 10⁵ N/C
c) 2 × 10⁶ N/C
d) 5 × 10⁵ N/C
Answer: b) 4 × 10⁵ N/C
Explanation: $E=F\mathrm{/}q=2\mathrm{/}(5\times {10}^{-6})=4\times {10}^5\text{N/C}$.

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32. Electric potential energy of two point charges 4 μC and 6 μC separated by 0.5 m in vacuum is:
a) 432 J
b) 432 × 10³ J
c) 432 × 10⁻³ J
d) 0.432 J
Answer: a) 432 J
Explanation: $U=k{q}_1{q}_2\mathrm{/}r=9\times {10}^9\times 4\times {10}^{-6}\times 6\times {10}^{-6}\mathrm{/}0.5=432\text{J}$.

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33. Electric field due to a dipole at a point on its perpendicular bisector is:
a) $E=kp\mathrm{/}{r}^2$ 
b) $E=kp\mathrm{/}{r}^3$ 
c) Zero
d) Infinite
Answer: b) $E=kp\mathrm{/}{r}^3$ 
Explanation: Field on perpendicular bisector: $E=kp\mathrm{/}{r}^3$ , perpendicular to dipole axis.

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34. Magnitude of electric field inside a charged conductor in electrostatic equilibrium:
a) Zero
b) Maximum at center
c) Minimum at surface
d) Depends on charge
Answer: a) Zero
Explanation: Charges reside on the surface; field inside conductor = 0.

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35. Electric field at a distance r from a line of charge (linear charge density λ) is:
a) $E=\lambda \mathrm{/}2\pi {ϵ}_{0}r$ 
b) $E=\lambda \mathrm{/}4\pi {ϵ}_0{r}^2$ 
c) $E=\lambda \mathrm{/}2{ϵ}_0{r}^2$ 
d) $E=\lambda \mathrm{/}4\pi r^2$ 
Answer: a) $E=\lambda \mathrm{/}2\pi {ϵ}_{0}r$
Explanation: Derived from Gauss’s law for cylindrical symmetry.

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36. Net flux through a cube enclosing a point charge q is:
a) Zero
b) q/ε₀
c) 6 q/ε₀
d) 3 q/ε₀
Answer: b) q/ε₀
Explanation: Gauss’s law: total flux through any closed surface = q_enclosed / ε₀.

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37. A 2 μC charge is moved through a potential difference of 5 V. Work done is:
a) 10 μJ
b) 7 μJ
c) 5 μJ
d) 2 μJ
Answer: a) 10 μJ
Explanation: $W=qV=2\times {10}^{-6}\times 5=10\times {10}^{-6}\text{J}=10\mu J$ .

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38. Torque on a dipole of moment p in a uniform field E at angle θ is:
a) pE sin θ
b) pE cos θ
c) p/E
d) E/p
Answer: a) pE sin θ
Explanation: Torque aligns dipole along the field direction.

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39. Electric field just outside a charged conductor surface is:
a) Zero
b) σ/ε₀ perpendicular to surface
c) Infinite
d) Along surface
Answer: b) σ/ε₀ perpendicular to surface
Explanation: Field is normal to surface, proportional to surface charge density.

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40. A hollow conducting sphere carries charge Q. Electric field outside the sphere at distance r is:
a) Zero
b) k Q/r²
c) k Q/r
d) k Q²/r²
Answer: b) k Q/r²
Explanation: Sphere behaves like a point charge at center for points outside.

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41. Capacitance of parallel plate capacitor depends on:
a) Plate area and separation
b) Material between plates
c) Both A & B
d) Charge on plates
Answer: c) Both A & B
Explanation: $C={ϵ}_0{ϵ}_{r}A\mathrm{/}d$ .

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42. Electric potential due to a point charge is:
a) V = kq/r²
b) V = kq/r
c) V = q/r²
d) V = kqr²
Answer: b) V = kq/r
Explanation: Work done per unit charge from infinity to distance r.

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43. A dipole in a non-uniform electric field experiences:
a) Force only
b) Torque only
c) Both force and torque
d) Neither
Answer: c) Both force and torque
Explanation: Torque aligns dipole; gradient in field exerts net force.

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44. Work done in separating two unlike charges from distance r to infinity is:
a) Positive
b) Negative
c) Zero
d) Depends on path
Answer: a) Positive
Explanation: Work is done against attractive force to separate unlike charges.

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45. Surface charge density is defined as:
a) Charge per unit volume
b) Charge per unit area
c) Charge per unit length
d) Total charge × area
Answer: b) Charge per unit area
Explanation: $\sigma =Q\mathrm{/}A$ .

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46. Electric field due to an infinite plane sheet of charge does not depend on:
a) Distance from sheet
b) Charge density
c) Dielectric constant
d) Direction
Answer: a) Distance from sheet
Explanation: For infinite sheet, $E=\sigma \mathrm{/}2{ϵ}_0$, independent of distance.

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47. Electric potential inside a uniformly charged solid sphere at distance r from centre:
a) V = kQ/R
b) V = kQ(3R² − r²)/2R³
c) Zero
d) kQ/r²
Answer: b) V = kQ(3R² − r²)/2R³
Explanation: Derived from integration of field inside sphere.

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48. The principle of superposition applies to:
a) Only potential
b) Only field
c) Both potential and field
d) Neither
Answer: c) Both potential and field
Explanation: Net potential or field due to multiple charges = algebraic sum (scalar for potential, vector for field).

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49. Field lines originate from:
a) Negative charges
b) Positive charges
c) Neutral objects
d) Both positive and negative equally
Answer: b) Positive charges
Explanation: By convention, field lines start from positive charges and end on negative charges.

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50. The work done in moving a charge along a closed path in an electrostatic field is:
a) Zero
b) Positive
c) Negative
d) Depends on path
Answer: a) Zero
Explanation: Electrostatic field is conservative; net work along closed path = 0.

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Electrostatics MCQs (Set-3: Advanced Level, Q51–75)

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51. Two point charges +Q and -Q form a dipole of length 2a. The magnitude of electric field at a point on the axial line, distance r from the center (r >> a) is:
a) $E=kQa\mathrm{/}{r}^2$ 
b) $E=k2Qa\mathrm{/}{r}^3$ 
c) $E=kQa\mathrm{/}{r}^4$
d) $E=kQ\mathrm{/}{r}^2$ 
Answer: b) $E=k2Qa\mathrm{/}{r}^3$ 
Explanation: Field along axial line: $E=(1\mathrm{/}4\pi {ϵ}_0)2p\mathrm{/}{r}^3$ , with dipole moment $p=Qa$.

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52. Potential at the midpoint of two equal and opposite charges +Q and -Q separated by 2a is:
a) Maximum
b) Minimum
c) Zero
d) Infinite
Answer: c) Zero
Explanation: Potential is scalar; contributions from +Q and -Q cancel at midpoint.

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53. Electric flux through a spherical surface of radius r surrounding a point charge q is:
a) q/r²
b) q/ε₀
c) 4π q
d) Zero
Answer: b) q/ε₀
Explanation: By Gauss’s law: $\mathrm{\Phi }=q_{\text{enclosed}}\mathrm{/}{ϵ}_0$.

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54. A charge q is placed at the center of a hollow conducting sphere. Electric field outside the sphere:
a) Zero
b) Same as if sphere not present
c) Depends on thickness
d) Depends on material
Answer: b) Same as if sphere not present
Explanation: Induced charges on sphere do not change field outside; behaves as point charge q.

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55. Electric field at a point on perpendicular bisector of a dipole, distance r >> a:
a) $E=kp\mathrm{/}{r}^2$ 
b) $E=kp\mathrm{/}{r}^3$ 
c) $E=0$ 
d) $E=k2p\mathrm{/}{r}^3$ 
Answer: b) $E=kp\mathrm{/}{r}^3$ 
Explanation: Perpendicular bisector field: $E=(1\mathrm{/}4\pi {ϵ}_0)p\mathrm{/}{r}^3$, perpendicular to axis.

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56. Net electric flux through a closed surface in a uniform external electric field:
a) Zero
b) Positive
c) Depends on shape
d) Infinite
Answer: a) Zero
Explanation: Uniform field → equal number of lines enter and exit → net flux = 0.

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57. Electric field between two oppositely charged infinite plates separated by d:
a) $E=\sigma \mathrm{/}{ϵ}_0$
b) $E=2\sigma \mathrm{/}{ϵ}_0$
c) $E=\sigma \mathrm{/}(2{ϵ}_0)$ 
d) Zero
Answer: a) $E=\sigma \mathrm{/}{ϵ}_0$
Explanation: Fields from plates add → uniform field between plates.

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58. Potential at a distance r from a uniformly charged thin ring (along axis):
a) V = k Q / r
b) V = k Q / √(r² + a²)
c) V = k Q r²
d) Zero
Answer: b) V = k Q / √(r² + a²)
Explanation: Potential is scalar; distance from each ring element: √(r² + a²).

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59. Work done in assembling 3 charges +Q, +Q, +Q at vertices of equilateral triangle side a:
a) 3 k Q² / a
b) k Q² / a
c) 2 k Q² / a
d) 6 k Q² / a
Answer: a) 3 k Q² / a
Explanation: Total potential energy: U = k(Q²/a + Q²/a + Q²/a) = 3 k Q² / a.

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60. A uniformly charged solid sphere, radius R, total charge Q. Electric field at distance r < R from center:
a) $E=kQ\mathrm{/}{r}^2$ 
b) $E=kQr\mathrm{/}{R}^3$ 
c) $E=0$ 
d) $E=kQ\mathrm{/}{R}^2$ 
Answer: b) $E=kQr\mathrm{/}{R}^3$ 
Explanation: Inside solid sphere: $E=(1\mathrm{/}4\pi {ϵ}_0)Qr\mathrm{/}{R}^3$.

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61. Electric potential at the center of a uniformly charged spherical shell:
a) Maximum
b) Zero
c) Infinity
d) Depends on shell radius
Answer: a) Constant (k Q / R)
Explanation: Potential inside shell = potential at surface.

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62. A dipole of moment p placed in uniform E-field at angle θ experiences:
a) Only torque
b) Only force
c) Torque and net force zero
d) Torque and net force non-zero
Answer: c) Torque and net force zero
Explanation: Uniform field → no net translational force; torque τ = pE sin θ.

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63. Capacitance of parallel plate capacitor filled with dielectric constant K:
a) C = ε₀ A / d
b) C = K ε₀ A / d
c) C = ε₀ d / A
d) C = A / (K ε₀ d)
Answer: b) C = K ε₀ A / d
Explanation: Dielectric increases capacitance by factor K.

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64. Electric field at point midway between +Q and +2Q, separated by 2 m:
a) E = 0
b) Directed toward +Q
c) Directed toward +2Q
d) Depends on medium
Answer: c) Directed toward +2Q
Explanation: Fields from like charges repel; stronger charge dominates direction.

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65. Electric field just outside the surface of a conductor with surface charge density σ:
a) E = 0
b) E = σ / ε₀ normal to surface
c) E = 2σ / ε₀ along surface
d) Infinite
Answer: b) E = σ / ε₀ normal to surface
Explanation: Field is perpendicular to surface.

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66. Electric potential energy of a system of two charges +q, -q separated by r:
a) Zero
b) -k q² / r
c) k q² / r
d) Depends on medium
Answer: b) -k q² / r
Explanation: Opposite charges → attractive → potential energy negative.

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67. Electric field due to an infinite line charge at distance r:
a) E = λ / 2 π ε₀ r
b) E = λ / 4 π ε₀ r²
c) E = λ / ε₀ r²
d) Zero
Answer: a) E = λ / 2 π ε₀ r
Explanation: Derived from Gauss’s law for cylindrical symmetry.

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68. Electric flux through any plane not enclosing charge in uniform field:
a) Zero
b) Non-zero
c) Depends on area
d) Infinite
Answer: b) Non-zero
Explanation: Flux depends on area orientation; not closed surface.

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69. Work done in moving a charge q around closed loop in static electric field:
a) Zero
b) Positive
c) Negative
d) Depends on path
Answer: a) Zero
Explanation: Electrostatic field is conservative.

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70. Electric field at a point due to system of two charges, q₁ and q₂:
a) Vector sum of fields of q₁ and q₂
b) Scalar sum of magnitudes
c) Zero always
d) Depends on medium only
Answer: a) Vector sum of fields of q₁ and q₂
Explanation: Superposition principle: fields add vectorially.

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71. Electric potential difference between two points in uniform field E separated by d along field line:
a) V = Ed
b) V = E/d
c) V = E² d
d) V = 0
Answer: a) V = Ed
Explanation: Potential difference along field: V = E × d.

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72. Electric field inside a hollow conductor with charge on outer surface:
a) Zero
b) Maximum at center
c) Depends on outer field
d) Same as outside
Answer: a) Zero
Explanation: Conductor in electrostatic equilibrium → field inside = 0.

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73. Electric field near edge of a thin charged sheet:
a) Uniform
b) Stronger near edges
c) Zero
d) Opposite to plate field
Answer: b) Stronger near edges
Explanation: Edge effects cause field to bulge; central region uniform.

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74. Electric field at a point due to an infinitely long uniformly charged rod:
a) Decreases with r²
b) Decreases with r
c) Constant
d) Increases with r
Answer: b) Decreases with r
Explanation: Field from line charge: E ∝ 1/r.

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75. Electric field at a point along the axial line of an electric dipole (r >> a):
a) E = k p / r²
b) E = k 2 p / r³
c) E = k p / r⁴
d) Zero
Answer: b) E = k 2 p / r³
Explanation: Axial line field of dipole: E = (1/4πε₀) 2p / r³.

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Electrostatics MCQs (Set-4: Expert Level, Q76–100)

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76. Two point charges +Q and -Q separated by distance 2a. Electric potential at point on perpendicular bisector (r >> a) is:
a) Zero
b) k Q / r
c) k Q a / r²
d) k Q / 2r
Answer: a) Zero
Explanation: Potential due to dipole along perpendicular bisector cancels: $V=V_{+}+V_{-}=0$ .

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77. Work done in bringing a charge q from infinity to a point at potential V is:
a) W = qV
b) W = V/q
c) W = q/V
d) Zero
Answer: a) W = qV
Explanation: Work done = charge × potential difference.

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78. Electric field at the centre of a uniformly charged semicircular ring of radius R and charge Q:
a) E = 0
b) E = k Q / R² along axis
c) E = 2 k Q / π R² perpendicular to diameter
d) E = k Q / 2 R
Answer: c) E = 2 k Q / π R² perpendicular to diameter
Explanation: Field contributions from semicircular elements add along perpendicular to diameter.

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79. Two point charges +3Q and -Q separated by distance d. Point where electric field is zero lies:
a) Between the charges
b) Outside nearer to -Q
c) Outside nearer to +3Q
d) At midpoint
Answer: b) Outside nearer to -Q
Explanation: Field cancels closer to weaker charge.

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80. Electric potential energy of three equal charges Q at vertices of equilateral triangle (side a):
a) 3 k Q² / a
b) k Q² / a
c) 2 k Q² / a
d) 6 k Q² / a
Answer: a) 3 k Q² / a
Explanation: U = k(Q²/a + Q²/a + Q²/a) = 3 k Q² / a.

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81. Solid non-conducting sphere of radius R carries uniform charge Q. Electric field at r > R:
a) E = k Q r²
b) E = k Q / r²
c) E = k Q / r
d) Zero
Answer: b) E = k Q / r²
Explanation: Outside sphere behaves like point charge.

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82. Electric field inside a thin spherical shell of uniform charge:
a) Zero
b) Maximum at center
c) Uniform
d) Varies linearly with radius
Answer: a) Zero

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83. Electric field due to infinite plane sheet of charge σ at distance x:
a) E = σ / 2 ε₀
b) E = σ / ε₀
c) E = σ / 4 ε₀
d) Zero
Answer: a) E = σ / 2 ε₀

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84. Electric flux through closed surface containing net charge +Q and -2Q:
a) -Q / ε₀
b) Q / ε₀
c) -2Q / ε₀
d) Zero
Answer: a) -Q / ε₀
Explanation: Flux = total enclosed charge / ε₀.

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85. Magnitude of torque on dipole in uniform E-field:
a) τ = p E sin θ
b) τ = p E cos θ
c) τ = p E
d) Zero
Answer: a) τ = p E sin θ
Explanation: Torque tends to rotate dipole to align with the field; τ = p × E × sin θ.

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86. Electric field at midpoint between +Q and -2Q separated by distance d:
a) Toward +Q
b) Toward -2Q
c) Zero
d) Depends on medium
Answer: b) Toward -2Q
Explanation: Field points toward stronger negative charge; magnitude cancels at point closer to weaker charge.

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87. Electric field on axis of ring of charge Q at distance x from center (radius R):
a) E = k Q x / (R² + x²)^(3/2)
b) E = k Q / R²
c) E = k Q / x²
d) Zero
Answer: a) E = k Q x / (R² + x²)^(3/2)
Explanation: Component along axis is sum of all ring elements: E = k Q x / (R² + x²)^(3/2).

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88. Electric field due to uniformly charged infinite plane capacitor:
a) Uniform between plates
b) Zero outside
c) Varies along plates
d) Maximum at edges
Answer: a) Uniform between plates
Explanation: Parallel plates create uniform field E = σ / ε₀ (central region), neglecting edge effects.

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89. Work done in moving a charge along equipotential surface:
a) Zero
b) Positive
c) Negative
d) Depends on path
Answer: a) Zero
Explanation: No potential difference along equipotential → no work is done.

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90. Electric field at centre of square with charges +Q at two adjacent corners, -Q at other two corners:
a) Zero
b) Non-zero
c) Maximum
d) Depends on distance
Answer: a) Zero
Explanation: Symmetry causes vector sum of fields from four charges to cancel at center.

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91. Potential difference between plates of parallel-plate capacitor:
a) V = Q / C
b) V = C / Q
c) V = Q C
d) Zero
Answer: a) V = Q / C
Explanation: Standard capacitor relation: V = Q / C.

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92. Capacitance of isolated spherical conductor of radius R:
a) C = 4 π ε₀ R
b) C = ε₀ / 4 π R
c) C = 4 π R
d) C = ε₀ R²
Answer: a) C = 4 π ε₀ R
Explanation: For isolated sphere, C = Q / V = 4 π ε₀ R.

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93. Electric field at surface of conductor with surface charge density σ:
a) E = σ / ε₀ normal
b) Zero
c) Along surface
d) Depends on shape only
Answer: a) E = σ / ε₀ normal
Explanation: Field is perpendicular to surface, magnitude E = σ / ε₀.

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94. Potential energy of dipole in uniform electric field at angle θ:
a) U = - p E cos θ
b) U = p E sin θ
c) U = 0
d) U = p E
Answer: a) U = - p E cos θ
Explanation: Dipole energy minimized when aligned with field; U = - p · E.

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95. A point charge q placed near grounded conducting plane. Induced charge on plane:
a) -q
b) q
c) 2q
d) Zero
Answer: a) -q
Explanation: Grounded plane induces equal and opposite charge to maintain zero potential.

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96. Electric potential at point along axis of circular ring of radius R (charge Q), distance x = 0:
a) V = k Q / R
b) V = k Q / x
c) V = 0
d) V = k Q / R²
Answer: a) V = k Q / R
Explanation: At centre, distance from every element = R → V = k Q / R (scalar sum).

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97. Net electric flux through cube in uniform electric field E, one face perpendicular to field:
a) Φ = E A
b) Zero
c) Φ = 2 E A
d) Depends on orientation
Answer: b) Zero
Explanation: Same number of field lines enter and exit → net flux = 0.

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98. Electric field just outside surface of spherical conductor:
a) Radially outward if positively charged
b) Zero
c) Tangential
d) Radially inward always
Answer: a) Radially outward if positively charged
Explanation: Field at surface normal to conductor, points away for positive charge.

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99. Electric potential at center of uniformly charged ring of radius R, total charge Q:
a) V = k Q / R
b) Zero
c) V = k Q / 2 R
d) V = k Q R
Answer: a) V = k Q / R
Explanation: Distance from all elements = R, potential adds as scalar → V = k Q / R.

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100. Electric field at a point near infinitely long line charge λ:
a) E = λ / (2 π ε₀ r)
b) E = λ / (4 π ε₀ r²)
c) E = λ / ε₀
d) Zero
Answer: a) E = λ / (2 π ε₀ r)
Explanation: Cylindrical symmetry → field decreases as 1/r, derived via Gauss’s law.

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