A circular loop and an infinitely long straight conductor carry equal currents, as shown in the figure . The net magnetic field at the centre of the loop is `B_(1)` when the current in the loop is clockwise and `B_(2)` when the current in the loop is anti - clockwise . Then `(B_(1))/(B_(2))` is

Options

A. `(15)/(19)`
B. `(13)/(15)`
C. `(13)/(17)`
D. `(17)/(19)`

Explanation

When current is clockwise then net magnetic field , `B_(1)= (mu_(0)i)/(2r) - (mu_(0)i)/(2pir) implies B_(1)= (mu_(0)i)/(2r) (1-(1)/(pi))`
Similarly when current is anti- clockwise
`B_(2)= (mu_(0)i)/(2r)(1+(1)/(pi))`
Now `(B_(1))/(B_(2))=((pi-1)/(pi))/((pi+1)/(pi))=((22)/(7)-1)/((22)/(7)+1)implies(B_(1))/(B_(2))=(15)/(29)`