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. `(pi I_(c))/(I_(e) R)`
B. `(I_(c) R)/(I_(e) pi)`
C. `(mu_(0) r)/(4r)`
D. `(I_(e) R)/(I_(e) pi)`

Answer

D

Explanation

Magnetic field at the centre `O` of the loop of radius `R` is given by
`B_(1) = (mu_(0) I_(e))/(2R)`
where `I_(e)` is the current flowing in the loop. Magnetic fied due to stragiht current carrying wire at a distance
`H, i.e.,` at the point `O` is given by `B_(2) = (mu_(0) I_(e))/(2pi H)`