Electric Charge & Coulomb’s Law questions with solutions

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• MCQmediumElectrostaticElectric Charge & Coulomb’s Law

  Two identical positive charges q are placed in a smooth horizontal circular groove at points separated by 90° at the centre. A third positive charge is placed in the groove so that all three charges are in tangential equilibrium immediately after release. The third charge must be placed:

  Options

  • Option A

    At 45° between the two original charges, with Q = 0.224q

  • Option B

    At 225°, opposite the midpoint of the minor arc, with Q = [(2+√2)³ᐟ²/2]q

  • Option C

    At 180° from either original charge, with Q = q

  • Option D

    At 270°, with Q = 2q

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• MCQeasyElectrostaticElectric Charge & Coulomb’s Law

  Two positive ions, each carrying a charge q, are separated by distance d. If F is the force of repulsion between them, the number of electrons missing from each ion is (e is the charge of an electron):

  Options

  • Option A

    4πε₀Fd²/e²

  • Option B

    √(4πε₀Fe²/d²)

  • Option C

    √(4πε₀Fd²/e²)

  • Option D

    4πε₀Fd²/q²

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• MCQmediumElectrostaticElectric Charge & Coulomb’s Law

  Two equal positive point charges q are fixed at x=±a. A particle of charge -Q and mass m is constrained to move only along the y-axis near the origin. For small |y|, the force on it is approximately:

  Options

  • Option A

    -(2qQ/4πε₀a³)y ĵ

  • Option B

    +(2qQ/4πε₀a³)y ĵ

  • Option C

    -(qQ/4πε₀a²) ĵ

  • Option D

    0

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• MCQmediumElectrostaticElectric Charge & Coulomb’s Law

  Particle B of charge Q and mass m is in equilibrium under weight and electrostatics force applied by a fixed charged A, which is directly beneath the particle B as shown in figure. When particle B is disturbed along vertical, the equilibrium is

  

  Options

  • Option A

    stable

  • Option B

    unstable

  • Option C

    neutral

  • Option D

    there can not be in equilibrium

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• MCQdifficultElectrostaticElectric Charge & Coulomb’s Law

  Twelve point charges are placed at the centres of the twelve edges of a cube of side r. With the cube oriented as in the given source figure, the charges on the four top edges are -q, +q, -q, +q; on the four vertical edges they are +q, +q, +q, -q; and on the four bottom edges they are +2q, -2q, +2q, -2q in the corresponding positions. A charge Q is placed at the centre of the cube. The magnitude of the electrostatic force on Q is:

  

  Options

  • Option A

    4k|qQ|/r²

  • Option B

    8k|qQ|/r²

  • Option C

    4√2k|qQ|/r²

  • Option D

    8√2k|qQ|/r²

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• MCQmediumElectrostaticElectric Charge & Coulomb’s Law

  If charge on each of two point charges is tripled and separation between them is doubled, by what factor will the mutual force between them change?

  Options

  • Option A

    9F/4

  • Option B

    -(9F/4)

  • Option C

    2×(9F/4)

  • Option D

    (9F/4)/2

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• MCQdifficultElectrostaticElectric Charge & Coulomb’s Law

  A fixed smooth non-conducting track is a quarter circle of radius R in a vertical plane. A small metal ball A is fixed at the bottom. An identical ball B can move on the track. Initially A and B are in contact and a total charge Q is given to A, which is shared equally, so each ball gets Q/2. Ball B finally comes to rest at a point where radius OB makes angle θ (<90°) with the downward vertical. Each ball has mass m. The charge Q is:

  

  Options

  • Option A

    8R√(2πε₀mg) · sin³ᐟ²(θ/2)

  • Option B

    4R√(2πε₀mg) · sin³ᐟ²(θ/2)

  • Option C

    8R√(πε₀mg) · sin(θ/2)

  • Option D

    4R√(πε₀mg) · sin³ᐟ²θ

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• MCQeasyElectrostaticElectric Charge & Coulomb’s Law

  Force between two point charges q₁ and q₂ placed in vacuum at ‘r’ cm apart is F. Force between them when placed in a medium having dielectric K = 5 at ‘r/5’ cm apart will be:

  Options

  • Option A

    F/25

  • Option B

    5F

  • Option C

    F/5

  • Option D

    25F

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• MCQmediumElectrostaticElectric Charge & Coulomb’s Law

  Four equal charges q₀ each, are kept fixed on the vertices of a square of side 'a'. Charge q₁ is kept at the center of the square as shown in the figure. Then which statement is correct ? (Here charge q₁ is restricted to move perpendicular to XY plane i.e. along z-axis)

  

  Options

  • Option A

    charge q₁ is always in stable equilibrium.

  • Option B

    charge q₁ is in unstable equilibrium.

  • Option C

    charge q₁ is always in stable equilibrium only if q₁ and q₀ have different (opposite) signs.

  • Option D

    charge q₁ is always in stable equilibrium only if q₁ and q₀ have same signs.

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• MCQmediumElectrostaticElectric Charge & Coulomb’s Law

  Two point charges q₁ = +3 μC and q₂ = -4 μC are located at position vectors r₁ = (2î+3ĵ+3k̂) m and r₂ = (î+ĵ+k̂) m, respectively. Taking 1 ÷ (4πε₀) = 9×10⁹ SI units, what is the force on q₂?

  Options

  • Option A

    (12î+24ĵ+24k̂)×10⁻³ N

  • Option B

    (4î+8ĵ+8k̂)×10⁻³ N

  • Option C

    (3î+6ĵ+6k̂)×10⁻³ N

  • Option D

    (-4î-8ĵ-8k̂)×10⁻³ N

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