A current carrying circular loop of radius ' R ' and current carrying long straight wire are placed in the same plane. I c and I w are the currents through circular loop and long straigh

Question

A current carrying circular loop of radius ' R ' and current carrying long straight wire are placed in the same plane. I c ​ and I w ​ are the currents through circular loop and long straight wire respectively. The perpendicular distance between centre of the circular loop and wire is ' d '. The magnetic field at the centre of the loop will be zero when separation ' d ' is equal to

TestHub · Accepted Answer

The magnetic field at the centre of the circular loop due to its own current is given by:

$B_{c} = \frac{μ _{0} I _{c}}{2 R}$

The magnetic field at the centre of the circular loop due to the long straight wire at a distance $d$ is given by:

$B_{w} = \frac{μ _{0} I _{w}}{2 π d}$

For the net magnetic field at the centre of the loop to be zero, the magnitudes of these two magnetic fields must be equal and opposite in direction.

$B_{c} = B_{w}$

$\frac{μ _{0} I _{c}}{2 R} = \frac{μ _{0} I _{w}}{2 π d}$

Rearranging the terms to solve for $d$ , we get:

$d = \frac{R I _{w}}{π I _{c}}$

Answer: $\frac{R I _{w}}{π I _{c}}$

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