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

Answer

a

Explanation

Magnetic field at the centre `O` of the loop of radius `R` is given by
`B_(1)=(mu_(0)I_(c ))/(2R)`
where `I_(c )` is the current flowing in the loop. Magnetic field due to straight current carrying wire distance `H`, i.e., at the point `O` is given by
`B_(2)=(mu_(0)I_(e ))/(2piH)`
For magnetic field to be zero at the centre of the loop,
`B_(1)=B_(2)`
i.e., `(mu_(0)I_(c ))/(2R)=(mu_(0)I_(e ))/(2piH)`
`H=(I_(e )R)/(piI_(c ))`