electric charge and coulamb's law questions with solutions

Showing 1–10 of 26 questions

• MCQdifficultElectrostaticselectric charge and coulamb's law

  A smooth fixed rod is inclined at angle θ to the horizontal. A fixed charge +Q is at its lower end. A bead of mass m and charge q can slide freely on the rod. Its equilibrium distance from Q is x₀. The angular frequency of small oscillations about equilibrium is:

  

  Options

  • Option A

    √[2g sinθ/x₀]

  • Option B

    √[g sinθ/x₀]

  • Option C

    √[2g cosθ/x₀]

  • Option D

    √[g cosθ/x₀]

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• MCQeasyElectrostaticselectric charge and coulamb's law

  A charge of 10 μC is divided into two parts and placed 1 cm apart. For maximum repulsive force, the two charges should be:

  Options

  • Option A

    7 μC and 3 μC

  • Option B

    8 μC and 2 μC

  • Option C

    9 μC and 1 μC

  • Option D

    5 μC and 5 μC

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• MCQeasyElectrostaticselectric charge and coulamb'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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  JEE Mains 2024 31 Jan Evening Shift

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• MCQmediumElectrostaticselectric charge and coulamb'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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  JEE Mains 2026 8 April Evening Shift

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• MCQmediumElectrostaticselectric charge and coulamb's law

  Two identical small conducting spheres carry positive charges q₁ and q₂ and are separated by distance d. The electrostatic force between them is F. They are brought into contact, then separated again to the same distance d. If the new force is F′, which statement is necessarily correct?

  Options

  • Option A

    F′ < F

  • Option B

    F′ = F for every q₁ and q₂

  • Option C

    F′ ≥ F, with equality only when q₁ = q₂

  • Option D

    F′ > F for every q₁ and q₂

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• MCQeasyElectrostaticselectric charge and coulamb's law

  Three identical positive point charges are placed at the vertices A, B and C of an equilateral triangle and released simultaneously. D is the midpoint of BC. Which statement correctly gives the initial directions of acceleration of the charges at A and B?

  

  Options

  • Option A

    At A along DA away from D; at B along the external angle bisector at B

  • Option B

    At A along AD toward D; at B parallel to AC

  • Option C

    At A perpendicular to AD; at B along BC

  • Option D

    At A along DA away from D; at B along BA

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• NumericmediumElectrostaticselectric charge and coulamb's law

  Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle θ with each other. When suspended in water, the angle remains the same. If density of the material of the sphere is 1.5 g cm⁻³, the dielectric constant of water is ______. [Density of water = 1 g cm⁻³]

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• MCQdifficultElectrostaticselectric charge and coulamb'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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• MCQdifficultElectrostaticselectric charge and coulamb's law

  A particle of mass m and positive charge q is attached to a light insulating thread of length L whose other end is fixed at O. A fixed positive charge Q is located a distance L vertically below O. The particle remains in equilibrium vertically above O with the thread taut, so the separation between q and Q is 2L. The minimum value of Q for which this inverted equilibrium is stable against a small horizontal displacement is:

  

  Options

  • Option A

    32πε₀mgL²/q

  • Option B

    16πε₀mgL²/q

  • Option C

    8πε₀mgL²/q

  • Option D

    4πε₀mgL²/q

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• MCQmediumElectrostaticselectric charge and coulamb's law

  Two identical conducting spheres are separated by distance l. One carries charge 4×10⁻⁸ C and the other is neutral. They are connected by a conducting wire and then the force between them is 9×10⁻³ N. Find l.

  Options

  • Option A

    4 cm

  • Option B

    4 m

  • Option C

    2 cm

  • Option D

    1 cm

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