The magnetic induction at point O of the given infinitely long current carrying wire shown in the figure below is

Options

A. `(mu_0 I)/(4pi R) ( 1 - (3pi)/(2) ) `
B. `(mu_0 I)/(2piR (1 + pi))`
C. `(mu_0I)/(4pi R) [ 1 + (3pi )/(2) ]`
D. `(mu_0 I)/(4pi R)`

Answer

C

Explanation

Magnetic field at point O = magnetic field of wire 1 + magnetic field of loop
` = (mu_0 I)/(4pi R) + (mu_0 I)/(4pi R) ((3pi)/(2) ) = (mu_0 I)/(4pi R) + 3/8 (mu_0 I)/(R ) = (mu_0 I)/(4pi R) ( 1 + (3pi)/(2) ) `