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For a uniformly charged thin spherical shell, the electric potential V radially away from the centre O of shell can be graphically represented as

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Important Questions on Electrostatics

HARD
A charge +q is distributed over a thin ring of radius r with line charge density λ=qsin2θπr. Note that the ring is in the XY-plane and θ is the angle made by r with the X-axis. The work done by the electric force in displacing a point charge +Q from the centre of the ring to infinity is
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The potential at the centre of a hollow, charged metal sphere of radius 5 cm, so that the potential on its surface 10 V, is
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Two concentric spherical conducting shells of radii R and ·2 R carry charges Q and 2 Q respectively. Change in electric potential on the outer shell when both are connected by a conducting wire is K=14πε0
EASY
A sphere has a constant electric potential V on its surface. If there are no charges inside the sphere, the potential at the centre of the sphere is
MEDIUM
A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of 4Q, the new potential difference between the same two surfaces is:
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n small metal drops of same size are charged to V volt each. If they coalesce to form a single large drop, then its potential will be
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N number of charges, +Q each, are placed maintaining equal distance on the circumference of a circle of radius R. The net electrostatic potential at the centre of the circle is
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Two spheres of unequal radii are supplied with equal quantity of charges. The potential will _______
HARD
Consider two charged metallic spheres S1 and S2 of radii R1 and R2, respectively. The electric fields E1 (on S1 ) and E2 (on S2 ) on their surfaces are such that E1E2=R1R2. Then the ratio V1 (on S1 )/V2 (on S2 ) of the electrostatic potentials on each sphere is:
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A charge Q is distributed over two concentric conducting thin spherical shells radii r and R R>r. If the surface charge densities on the two shells are equal, the electric potential at the common centre is : 

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MEDIUM

Four point charge (with equal magnitude of charge of 5 C; but with different signs) are placed at four corners of a square of side 10 m. Assuming that the square is centered at the origin and the configuration of the charges are as given in the figure, the potential and the magnitude of electric field at the origin, respectively are

[Note k=14πε0

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MEDIUM
A charge Q is distributed over three concentric spherical shells of radii a, b, c a<b<c such that their surface charge densities are equal to one another.

The total potential at a point at distance r from their common centre, where r<a, would be:
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What will be the potential at the centre of the sphere when a hollow metal sphere of radius 10 cm is charged such that the potential on its surface is 80 volts?
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A spherical drop of mercury having a potential of 2.5 V is obtained as a result of merging 125 droplets. The potential of constituent droplets would be
MEDIUM
The two thin coaxial rings, each of radius a and having charges +Q and -Q respectively are separated by a distance of s. The potential difference between the centres of the two rings is :
MEDIUM
N identical spherical drops charged to the same potential V are combined to form a big drop. The potential of the new drop will be
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Charge on the outer sphere is q and the inner sphere is grounded. The charge on the inner sphere is q', for r2>r1. Then
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Concentric metallic hollow spheres of radii R and 4R hold charges Q1 and Q2 respectively. Given that surface charge density of the concentric spheres are equal, the potential difference VR-V(4R) is:
HARD
A uniformly charged ring of radius 3a and total charge q is placed in xy plane centred at origin. A point charge q is moving towards the ring along the z- axis and has speed v at  z=4a . The minimum value of v such that it crosses the origin is: