Question

if a point charge -q with mass m is released from point p which is at distance 4a above the center of a charged ring which has a radius of 3a and +5q charge which is uniformly distributed on it,what will be the velocity of that point charge when it pass the center of the charged ring?

Answer 1

Neglecting the effect of gravity,

the force here is conservative in nature. So total energy will be conserved.

Write the initial total energy when the particle is released.

Initially kinetic energy=0

Write the final total energy when the particle is passing through the centre. There will be a kinetic energy term in this equation.

Equate the two equations since total energy is constant in time, and your speed will come from the kinetic energy term.

Try this! Make sure you write the electrostatic potential energy terms properly.

Answer 2

the problem is I don't know how to calculate the electrostatic potential energy for a ring.to calculate it I should know the electric field of the ring at any point on the Z axis .according to Gauss law I have to take an Gaussian surface to calculate E. but I can't determine proper surface for this case.

Answer 3

Don't use a Gaussian surface.

To find the electric field of the ring, consider a small element of the ring with charge dq.

Write the electric field of this charge dq at a point on the axis of the ring (let it be z-axis), using Coulomb's law.

This electric field will have two components, one along the axis and another perpendicular to the axis(take appropriate angle to find the components).

When you perform the integration over the whole ring (charge), you will find out that the perpendicular components cancel out and the component along the axis add up.

Try this method.