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Question

A charge +Q is uniformly distributed over a thin ring of radius R. Find the velocity of a negative point charge −Q at the moment it passes through the centre of the ring if it has mass m and was initially at rest at infinity on the axis of the ring.

A
Q2kmR
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B
0
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C
2QkmR
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D
2kQmR
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Solution

The correct option is A Q2kmR
Given that,
Radius of the ring =R
Mass of charge Q=m

Let the velocity of the charge Q is v when it passes through the centre of the ring.

The potential energy at the centre of the ring, U=k(Q)(Q)R=kQ2R

This is the final potential energy, so, Uf=kQ2R

The initial potential energy when charge Q is at infinite distance away from the ring is zero. So, Ui=0.


Now, we know from conservation of Mechanical energy for the system,
Decrease in potential energy = Increase in kinetic energy

0(kQ2R)=12mv20

12mv2=kQ2R

v=Q2kmR

Hence, option (b) is correct

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