electric charge and coulamb's law questions with solutions

Showing 1–10 of 30 questions

• MCQdifficultElectrostaticelectric 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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• MCQdifficultElectrostaticelectric charge and coulamb's law

  Two identical positive charges Q are fixed on the x-axis at x = -a and x = +a. A particle of mass m and charge q is placed near the origin. For q > 0 it performs small oscillations along the x-axis with period T₁. If q < 0, it performs small oscillations along the y-axis with period T₂. The ratio T₁/T₂ is:

  Options

  • Option A

    1/√2

  • Option B

    1

  • Option C

    √2

  • Option D

    2

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• NumericmediumElectrostaticelectric charge and coulamb's law

  A point charge q₁ = 4q₀ is placed at origin. Another point charge q₂ = -q₀ is placed at x = 12 cm. Charge of proton is q₀. The proton is placed on x-axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is _____ cm.

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  JEE Mains29 January 2023Shift 1Morning Shift

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• Multi-correctmediumElectrostaticelectric charge and coulamb's law

  A uniformly charged ring of radius R and total charge q contains a point charge Q at its centre. Consider one semicircular half of the ring. Which statements are correct?

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  • Option A

    The net force exerted by Q on one semicircular half is kQq/(πR²)

  • Option B

    The increase in the total separating force between the two semicircular halves is kQq/(πR²)

  • Option C

    The increase in tension at each cut end is kQq/(2πR²)

  • Option D

    The net force exerted by Q on one semicircular half is zero

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• MCQmediumElectrostaticelectric 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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• MCQmediumElectrostaticelectric charge and coulamb's law

  Two horizontal metal plates A and B are separated by (12 ÷ π) cm, with plate A above plate B. An atomizer sprays positively charged oil droplets horizontally between the plates. Each droplet has radius 1 mm, density 1.5 g·cm⁻³ and charge 5 nC. Neglect air resistance and take g = 10 m·s⁻². Which pair of plate potentials keeps the droplets from descending?

  Options

  • Option A

    V(A) = 100 V and V(B) = 580 V

  • Option B

    V(A) = 580 V and V(B) = 100 V

  • Option C

    V(A) = 60 V and V(B) = 400 V

  • Option D

    V(A) = 0 V and V(B) = -200 V

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• MCQmediumElectrostaticelectric charge and coulamb's law

  Two positively charged particles of masses m₁ = 2m and m₂ = m are suspended from a common point by two light strings of unequal lengths. In equilibrium both particles are at the same horizontal level and the angle between the strings is 45°. If F is the electrostatic force exerted by m₁ on m₂, then F/(mg) is:

  

  Options

  • Option A

    (√17 - 3)/2

  • Option B

    (√17 + 3)/2

  • Option C

    1/2

  • Option D

    √2

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• MCQmediumElectrostaticelectric charge and coulamb's law

  Six identical positive charges q are placed at the six vertices A, B, C, D, E and F of a regular hexagon of circumradius R. The magnitude of the net electrostatic force on the charge at vertex A is F. First, the charge at A is moved to the centre; let the force magnitude on it there be F₁. Then the charge at E is also moved to the centre, so that the charge present at the centre becomes 2q; let the force magnitude on this central charge due to the charges remaining at the vertices be F₂. Which ordered pair (F₁,F₂) is correct?

  

  Options

  • Option A

    (12F/(12√3+7), 24F/(12√3+7))

  • Option B

    (F, 2F)

  • Option C

    (12F/(12√3+7), 12F/(12√3+7))

  • Option D

    (24F/(12√3+7), 12F/(12√3+7))

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• Multi-correctmediumElectrostaticelectric charge and coulamb's law

  Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is α. The spheres are now immersed in a dielectric liquid of density 800 kg m⁻³ and dielectric constant 21. If the angle between the strings remains the same after the immersion, then

  Select all that apply

  • Option A

    electric force between the spheres remains unchanged

  • Option B

    electric force between the spheres reduces

  • Option C

    mass density of the spheres is 840 kg m⁻³

  • Option D

    the tension in the strings holding the spheres remains unchanged

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• NumericmediumElectrostaticelectric charge and coulamb's law

  Two identical charged spheres are suspended by string of equal lengths. The string make an angle of 37° with each other. When suspended in a liquid of density 0.7 g/cm³, the angle remains same. If density of material of the sphere is 1.4 g/cm³, the dielectric constant of the liquid is _________ (tan37° = $\frac{3}{4}$).

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  JEE Mains 2024 30 Jan Evening Shift

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