Question

A circular loop has radius R and carries current I as shown in figure. In order that the net magnetic field at the centre of the loop is zero, the current in wire AB should have magnitude ______.

Options

• 2πI, along +X-axis

• 2πI, along −X-axis

• πI, along +X-axis

• πI, along −X-axis

Answer 1

A circular loop has radius R and carries current I as shown in figure. In order that the net magnetic field at the centre of the loop is zero, the current in wire AB should have magnitude 2πI, along −X-axis.

Explanation:

The magnetic field produced by a long straight wire carrying current I_AB at a perpendicular distance d = 2R is given by:

B_wire = `(mu_0 I_(AB))/(2 pi d)`

= `(mu_0 I_(AB))/(4 pi R)`

Equating the magnitudes of the two magnetic fields:

`(mu_0 I)/(2 R) = (mu_0 I_(AB))/(4 pi R)`

I_AB = `(mu_0 I)/(2 R) xx (4 pi R)/mu_0`

= 2πI

The current in wire AB should have a magnitude 2πI, along +X-axis