Circular loop of a wire and a long straight wire carry current `I_(c )` and `I_(e )`respectively as shown in figure. Assuming that these are placed in the same plane. The magnetic field will be zero at the centre of the loop when the separation `H` is:

Options

A. `(I_(e) R)/(I_(c) pi)`
B. `(I_(c) R)/(I_(e) pi)`
C. `(n I_(c))/(I_(e) R)`
D. `(I_(e) pi )/(I_(c) R)`

Answer

A

Explanation

Field due to loop
`B_(1) = (mu_(0) I_(c))/(2R) odot`
Field due to wire `B_(2) = (mu_(0) I_(e))/(2pi H) otimes`
Since at centre B = `0 implies (mu_(0) I_(c))/(2R) = (mu_(0) I_(e))/(2pi H) implies H = (I_(e) R)/(pi I_(c))`