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. `(l_(e)R)/(l_(e)pi)`
B. `(l_(e)R)/(l_(e)pi)`
C. `(pil_(e))/(l_(e)R)`
D. `(l_(e)pi)/(l_(e)R)`

Answer

A

Explanation

Magnetic field du to a circular loop at the centre of the loop is `B_(1)'=(mu_(0))/(4pi) (2pil_(c))/(R)`
Magnetic field due to a stright line at the centre of the loop is `B_(2)=(mu_(0)2l_(e))/(4piH)`
Both these field act in opposite directio hence total magnetic field at the centre of the loop is
`B=B_(1)-B_(2)=(mu_(2)2pil_(e))/(4pir) -(mu_(0)2l_(e))/(4piH)`
B=0 given
`:. (mu2pil_(e))/(4piR)=(mu_(0)2l_(e))/(4piH) or, H-(l_(e)R)/(pil_(e))`