Question

(a) Calculate the electrostatic force on a uniformly charged rod of length 2l, and charge q which lies along the axis of a uniformly charged ring of radius R and charge q'. The centers of the charged rod and the rings are displaced by z = z₀. (b) Show that if z₀ >> l, is satisfied, then the expression of calculated force reduces to that between point charges.

Answer 1

a )

the radius of the ring is R, rod length is 2 L

the angle θ is tangent to the circle

the tangent distance is ( 4 L² + R² )^1/2  

the equation of force is

F = Q² / 4 πε ( 4 L² + R² )

F = 2 Q² L / 4 πε ( 4 L² + R² )^3/2  

b )

Z_o is the distance from the center of the circular ring to a center of the charge of the rod

then the force will be " F "

F = Q² Z_o / 4 πε ( 4 L² + R² )^3/2