Question

There are four coils of wire being used as electromagnets. They all have the same size and are made up of the same material but have a different number of loops. Which coil will produce a magnetic field with the maximum strength when the same amount of current passes through all coils?

Answer 1

Answer:

The coil with the maximum number of loops will produce the magnetic field with the maximum strength.

Explanation:

The magnetic field produced by a current-carrying coil at a point on the axis which is passing through its center and perpendicular to its plane is given by

$\rm B=\dfrac{\mu_o N I }{2}\ \dfrac{R^2}{(r^2+R^2)^{3/2}}.$

where,

• $\mu_o$ = magnetic permeability of the free space.
• N = number of loops of the coil.
• I = current flowing through the coil.
• R = radius of the coil.
• r = distance of the point where the magnetic field is to be found from the center of the coil.

Now, it is given that all the four coils have the same size, means same radius R, same material, means same permeability for all the coils, and the same amount of current is passing through all the coils, means same current I.  

The magnetic field of all the four coils is differing only due to the number of loops N.

Thus, the coil with the maximum number of loops N will produce the magnetic field with the maximum strength.