The magnetic field at O due to current in the infinite wire forming a loop as a shown in Fig.

Options

A. `(mu_0I)/(2pid) (cos phi_1+cos phi_2)`
B. `(mu_0)/(4pi) (2I)/d (tan theta_1+tan theta_2)`
C. `(mu_0)/(4pi) I/d (sin phi_1+sin phi_2)`
D. `(mu_0)/(4pi) I/d (cos theta_1+cos theta_2)`

Answer

A

Explanation

(a) Using `B=(mu_0i)/(4pia)[sin theta_1+sin theta_2]`
But ` theta_1+phi_1=90^@ or theta_1=90^@-phi,`
`sin theta_1= sin(90^@-phi_1)=cos phi_1`
Similarly, `sin theta_2=cos phi_2`
`B_(n et)=(mu_0I)/(2pia)(cos phi_1+cos phi_2)`