From a cylinder of radius R, a cylider of radius `R//2` is removed, as shown in Fig. Current flowing in the remaining cylinder is I. Then, magnetic field strength is

Options

A. zero at point A
B. zero at point B
C. `(mu_(0)I)/(3piR)` at point A
D. `(mu_(0) I)/(3 pi R)` at point B

Answer

C, D

Explanation

For cylinder ,
`B = (mu_(0) ir)/(2 pi R^(2)) , r lt a`
`= (mu_(0) i)/(2 pi r) ' r ge a`
We can consider the given cyliner as a combination of two cylinders. One of radius 'R' carrying current `I` in one direction and other of radius `(R)/(2)` carrying current `(I)/(3)` in both directions
At point A :
`B=(mu_(0)(I//3))/(2 pi(R//2))+0=(mu_(0)I)/(3 pi R)`
Also point B :
`B = (mu_(0))/(2) ((4I//3)/(pi R^(2)))((R)/(2))+0=(mu_(0)I)/(3 pi R)`.