Question

A rod of length 'l' has charge distribution on it such that linear charge density λ=kx.; 'k' is a constant and 'x' is the distance of a point from the end of the rod where no charge exists. The rod has mass 'm' and the mass distribution is uniform. The rod is now rotated with an angular velocity ω about a axis passing through the end of the rod where no charge exists and this axis is perpendicular to the length of the rod. If I is the equivalent current then find the value of I.

Answer 1

Answer:

As coulomb's force is an action reaction pair, so force experienced by the linear charge is equal and opposite to the force experienced by point charge q. Here, we are computing electric force experienced by q due to the charge.

Considered a small element on line charge as shown, then force experienced by q due to this element is,

F=∫dF=∫

R

R+L

4πε

0

r

2

qλdr

=

4πε

0

R(R+L)

qλL

dF=

4πε

0

r

2

qλdr

On integrating between the given limits, we will get

F=

4πε

0

R(R+L)

qλL