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. `(mu_0I)/(3piR)` at point B
B. `(mu_0I)/(2piR)` at point A
C. zero at point B
D. zero at point A

Answer

D

Explanation

(d) Current density:`rho=1/(piR^2-pi(R//2)^2) implies rho=(4I)/(3piR^2)`

Current in smaller cylinder (if there were): `I_1=rhopi(R/2)^2 =I/3`
For A: `B_A=B_("whole-cylinder")-B_("small-cylinder")`
`implies B_A=0-(mu_0(I/3))/(2pi(R//2))=-(mu_0I)/(3piR)`
For B: `B_B=B_("whole -cylinder")-B_("small-cylinder")`
`=(mu_0(I+I//3)(R//2))/(2piR^2)-0=(mu_0I)/(3piR)`