Circular loop of a wire and a long straight wire carry currents and respectively as shown in figure. Assuming that these are placed in the same plane, the magnetic fields will be zero at the centre of the loop when separation H Circular wire Straight wire

Options

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

Answer

A

Explanation

Magnetic fieds at the centre O of the curcular current loop is `B_(1)=mu_(0)/(4pi)(2piI_(c))/("R")`
Magnetic field at the centre O of the circular loop due to current through long straight wire is `B_(2)=(mu_(0))/(4oi)(2I_(e))/(H)`.
As the resultant magnetic field at O is zero (given) hence `B_(1)` and `B_(2)` must be equal in magnitude and opposite in direction,So
`(mu_(0))/(4pi)(2piI_(c))/("R")=(mu_(0))/(4pi)(2Ie_(e))/(H)=(I_(e)R)/(piI_(c))`