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. `(muoI)/(3piR)` at point `A`
D. `(muoI)/(3piR)` at point `B`

Answer

D

Explanation

For cylinder:
`B=(mu_(0)ir)/(2piR^(2)), r lt a`
`=(mu_(0)i)/(2piR^(2)), rgea`
We can consider the given cylinder as a combination of two cylinders. One of radius `'R'` carrying current `I` in the one direction and other of radius `(R )/(2)` carrying current `I/3` in both directions.
At point `A:B=(mu_(0)(1//3))/(2pi(R//2))+0=(mu_(0)I)/(3piR)`
At point `B:B=(mu_(0))/(2pi)((4I//3)/(piR^(2)))(R/2)+0=(mu_(0)I)/(3piR)`