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Electric Charges and Fields: questions with answers

Class 12 Physics, Chapter 1 (NCERT). 15 questions by concept, 2 with pictures. Open “Show answer” for the answer and why.

How to teach this chapter · Common misconceptions & worked visual for this chapter

Charge quantisation and counting carriers

Question 1

An isolated body is claimed to have net charge (300+1/2)e, where e is the elementary charge. Which assessment is correct?

  1. (a)Allowed: net charge can be any real multiple of e
  2. (b)Not allowed: all net charges must be negative
  3. (c)Allowed: only the sign of net charge is restricted
  4. (d)Not allowed: the net charge is not an integral multiple of e
Show answer

(d) Not allowed: the net charge is not an integral multiple of e

The claimed charge has a half-integer multiple of e. A freely isolated body has an integral number of excess or missing elementary carriers.

Charging, conduction and charge conservation

Question 2

An initially neutral glass rod acquires charge +10e when rubbed with silk; e is the elementary charge. Which transfer explains this?

  1. (a)10 protons moved from glass to silk
  2. (b)10 electrons moved from glass to silk
  3. (c)10 electron-proton pairs moved from silk to glass
  4. (d)10 electrons moved from silk to glass
Show answer

(b) 10 electrons moved from glass to silk

Positive charging means an electron deficit. Losing 10 electrons leaves the glass with charge +10e.

Coulomb force and inverse-square comparisons

Question 3

Two fixed point charges exert force magnitude F at separation r. Their charges remain unchanged and their separation becomes 3r. What is the new force magnitude?

  1. (a)F/9
  2. (b)F/27
  3. (c)9F
  4. (d)F/3
Show answer

(a) F/9

Coulomb force is proportional to 1/r². Replacing r by 3r divides F by 9.

Vector superposition and symmetry

Question 4

The diagram shows two perpendicular electric-field contributions at P. What is their resultant magnitude?

9 N/C12 N/CP
  1. (a)21 N/C
  2. (b)3 N/C
  3. (c)15 N/C
  4. (d)75 N/C
Show answer

(c) 15 N/C

Perpendicular components combine by Pythagoras: sqrt((3u)²+(4u)²)=5u, not 3u+4u.

Electric field, test charge and particle motion

Question 5

A charge -3 nC is placed in a uniform electric field 100 N/C directed towards +x. What is its force?

  1. (a)300 nN towards -x
  2. (b)Zero nN
  3. (c)300 nN towards +x
  4. (d)100/3 nN towards -x
Show answer

(a) 300 nN towards -x

Use F=qE. Its magnitude is |q|E, and the negative sign reverses the field direction.

Meaning and consistency of electric field lines

Question 6

A proposed electrostatic field map has two field lines crossing at a charge-free point, with different tangent directions. Which judgement is correct?

  1. (a)Invalid only if the two lines have different colours
  2. (b)Valid whenever both charges creating the field have the same sign
  3. (c)Invalid: it assigns two directions to the resultant electric field at one point
  4. (d)Valid: two source fields should be shown by crossing resultant-field lines
Show answer

(c) Invalid: it assigns two directions to the resultant electric field at one point

Each field line is tangent to the unique resultant field. Distinct crossing tangents would assign incompatible directions at the same regular point.

Oriented area and electric flux

Question 7

A plane area of 2 m² is in a uniform field 100 N/C making 30° with the plane. Choose the normal with a positive field component. What is the flux?

  1. (a)Zero N m²/C
  2. (b)100 N m²/C
  3. (c)200 N m²/C
  4. (d)200√3/2 N m²/C
Show answer

(b) 100 N m²/C

The angle with the normal is 60°. Thus flux=EA cos60°=EA/2, not EA cos30°.

Axial and equatorial dipole fields

Question 8

A far axial point is at distance r_a from a short dipole. A far equatorial point is at distance r_e. Their field magnitudes are equal. What is r_a³:r_e³?

  1. (a)8:1
  2. (b)1:1
  3. (c)1:2
  4. (d)2:1
Show answer

(d) 2:1

Equate 2kp/r_a³=kp/r_e³. Cancelling kp gives r_a³=2r_e³.

Electric dipole moment and its direction

Question 9

The diagram shows two equal opposite charges on the x-axis. In which direction does their dipole moment point?

+q-q-15 cm+15 cmx
  1. (a)Towards -x
  2. (b)It has no direction because total charge is zero
  3. (c)Towards +x
  4. (d)Towards +y
Show answer

(a) Towards -x

Dipole moment points from the negative charge position to the positive charge position.

A dipole in a uniform electric field

Question 10

A permanent dipole is initially parallel to a uniform electric field. It is then turned until perpendicular to that field. How do the torque magnitudes compare?

  1. (a)Initially and finally pE
  2. (b)Initially and finally zero
  3. (c)Initially pE; finally zero
  4. (d)Initially zero; finally pE
Show answer

(d) Initially zero; finally pE

Torque magnitude is pE sin(theta). It is zero at 0° and maximum, pE, at 90°.

Continuous charge distributions

Question 11

A uniformly charged wire segment has linear charge density 6 nC/m and length 2 m. What is the charge on the segment?

  1. (a)3 nC
  2. (b)8 nC
  3. (c)12 nC
  4. (d)-12 nC
Show answer

(c) 12 nC

Linear density is charge per length. Multiply by length: Q=lambda L.

Gauss law for spherical charge distributions

Question 12

A uniformly charged thin spherical shell has nonzero total charge. Which argument correctly establishes its field at a point strictly inside?

  1. (a)Treat all shell charge as concentrated at the centre and use kQ/r² inside
  2. (b)Opposite sides of the shell must carry opposite charge signs
  3. (c)Zero flux always implies zero field for every possible charge arrangement
  4. (d)A centred Gaussian sphere encloses no charge, and spherical symmetry makes E uniform on it, giving E=0
Show answer

(d) A centred Gaussian sphere encloses no charge, and spherical symmetry makes E uniform on it, giving E=0

Both facts matter: there is no enclosed shell charge, and spherical symmetry allows the field magnitude to be taken outside the flux integral. Zero net flux alone would not suffice for an arbitrary arrangement.

Gauss law: enclosed charge, net flux and symmetry

Question 13

A closed surface encloses no charge. An external point charge is moved closer while remaining strictly outside. Which statement is correct?

  1. (a)Gauss law ceases to apply because the external field is nonuniform
  2. (b)The external charge adds nonzero net outward flux as it approaches
  3. (c)The field on the surface may change, but the total outward flux remains zero
  4. (d)The field must be zero at every point on the surface
Show answer

(c) The field on the surface may change, but the total outward flux remains zero

The enclosed charge remains zero. External field lines enter and leave the surface, so local changes cancel in the total flux.

Gauss law for a plane sheet and parallel sheets

Question 14

Two parallel infinite sheets have surface charge densities +σ and -σ. Two points inside the gap lie at different distances from the positive sheet. Which statement is correct?

  1. (a)The point nearer the positive sheet has a stronger resultant field because sheet fields decay with distance
  2. (b)Both points have the same field magnitude σ/ε0, directed from the positive sheet to the negative sheet
  3. (c)Both points have zero field because the two sheets have opposite charges
  4. (d)The fields at the two points point in opposite directions
Show answer

(b) Both points have the same field magnitude σ/ε0, directed from the positive sheet to the negative sheet

Each sheet supplies a distance-independent field σ/(2epsilon0). Within the gap their directions agree, so the total is σ/epsilon0 everywhere.

Gauss law for an infinite charged wire

Question 15

A Gaussian cylinder has the same axis as an infinitely long, uniformly charged straight wire. Which part of the cylinder carries the electric flux?

  1. (a)The two flat end caps; the curved wall has zero flux
  2. (b)No part carries flux because the surface is closed
  3. (c)The curved wall; the two flat end caps have zero flux
  4. (d)All three parts have equal flux
Show answer

(c) The curved wall; the two flat end caps have zero flux

The wire field is radial. It is normal to the curved wall and tangent to both end caps, so only the curved wall contributes.

Common misconception in Electric Charges and Fields

Open full misconception guide →

Does zero enclosed charge mean zero field everywhere on a surface?

Wrong

If the net electric flux is zero, the electric field must vanish at every point of the surface.

Why it feels right. Gauss's law gives zero for the total, so I assign zero to every contribution.

Right

Flux sums signed contributions over the surface. Fields may cross it even when the sum is zero.

Worked example

Uniform field crosses both faces. Opposite outward normals make the flux contributions cancel.
  1. Place a closed box in a uniform electric field.
  2. Field enters one face and leaves the opposite face.
  3. The contributions cancel although the field is present at both faces.