The concepts required to solve this problem is magnetic field due to a circular coil.
Initially, use the expression of the magnetic field at the center of the circular coil and rearrange it to find the expression of current flowing in the coil. Then, substitute the values in the expression to find the value of current.
Then, use the expression of the magnetic field at the point on the axis of the circular coil and substitute the values to find the magnetic field at that point.
Fundamentals
The expression of the magnetic field at the center of the circular coil is given as follows:
B=2rμonI
Here, μo is the permeability of free space, n is the number of turns, I is the current, and r is the radius of the coil.
The expression of the magnetic field at a distance x from the center of the coil along the axis of the coil is as follows:
B=2μonI(x2+r2)23r2
Here, μo is the permeability of free space, n is the number of turns, I is the current, x is the distance of the point at which the magnetic field is to be found from the center of the coil, and r is the radius of the coil.
(a)
The expression of the magnetic field at the center of the circular coil is given as follows:
B=2rμonI
Here, μo is the permeability of free space, n is the number of turns, I is the current, and r is the radius of the coil.
Rearrange the above expression for I.
I=μon2Br
Substitute 5×10−2T for B, 2.10cm for r, 4π×10−7H/mfor μo, and 830 for n in the above expression.