The dimensions of the coil were changed so that its inductance increased by 4 times.

The dimensions of the coil were changed so that its inductance increased by 4 times. the current in the coil has not changed. how the energy of the magnetic field has changed.

The energy of the magnetic field W, J, can be determined by the formula:

W = L * I ^ 2/2,

where L is the inductance of the coil, H;

I – current strength, A.

Then for two cases – L1 = L and L2 = 4 * L – with constant current I we have:

W1 = L1 * I ^ 2/2 = L * I ^ 2/2;

W2 = L2 * I ^ 2/2 = 4 * L * I ^ 2/2.

Dividing the second expression by the first, we find how many times the energy of the magnetic field has increased:

W2 / W1 = (4 * L * I ^ 2/2) / (L * I ^ 2/2) = 4.