Question

A long straight wire is turned into a loop of radius R=10cm, as shown. If a current of 8A is passed through the loop, find the magnetic field at the centre C of the loop.

Answer 1

The magnetic moment of a current carrying coil is given by μ = niAk

Where,

n is the number of loops

i is the current throught the coil

A is the area of cross section of the coil

k is the unit vector along the direction of the magnetic moment

Since there is only one loop, n=1

Therefore,

μ =8*π(0.1)^2 k

=0.08π k

And to find k, imagine the coil in front of you such that the current in the coil is flowing in counter-clockwise direction (as seen by you)

Now curl your fingers along the circumference of the loop, you thumb will point in the direction of k which is also the direction of the magnetic moment of the loop

Hope this helps ;)