Question

A 0.20-cm radius cylinder, 3.0 cm long, is wrapped with wire to form an inductor. At the instant the magnetic field in the interior is 5.0 mT. the permeability of free space is Mo = 411 x 10-7 T.m/A, how much the energy stored in the field?

A. 7.5 x 10^-6j
B. 7.5 x 10^-4 ]
C. 0
D. 3.8 x 10-6

Answer 1

To calculate the energy stored in the magnetic field of the inductor, you can use the formula E = 0.5 * L * I^2, where E is the energy stored, L is the inductance, and I is the current flowing through the inductor.

Step-by-step explanation:

To calculate the energy stored in the magnetic field of the inductor, we can use the formula E = 0.5 * L * I^2, where E is the energy stored, L is the inductance, and I is the current flowing through the inductor. First, we need to find the inductance of the cylinder:

L = μ0 * N^2 * A / l

where μ0 is the permeability of free space, N is the number of wire turns, A is the cross-sectional area of the cylinder, and l is the length of the cylinder.

Using the given values and substituting them into the formulas, we get:

L = (4π×10^-7 T×m/A) * (N^2 * πr^2) / l

Next, we can calculate the energy stored in the magnetic field:

E = 0.5 * L * I^2

Substituting the given values, we get:

E = 0.5 * (4×10^-7 T×m/A) * ((N^2 * πr^2) / l) * I^2

We can now solve for the energy stored in the field.