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_lR)/(I_cpi)`
B. `(I_cR)/(I_lpi)`
C. `(I_cpi)/(I_lR)`
D. `(I_lpi)/(I_cR)`

Explanation

Using Ampere's circuital law. Mag. field at centre of circular coil due to long straight wire
`B_1=(mu_0I_l)/(2piH)`
Due to circular coil, mag. field at the centre O is given by `B_2=(mu_0I_c)/(2R)`
Now `B_1` and `B_2` are is opposite directions. For resultant to be zero, `B_1=B_2`
`(mu_0I_l)/(2piH)=(mu_0I_c)/(2R)`, i.e., `H=(I_lR)/(I_cpi)`