A coil with a self-inductance of 5.0 henrys and a resistance of 200 ohms carries a steady current of 3.0 amps. What is the energy stored in the magnetic field of the coil?
We have then a coil of conducting material which carries a current, whose value we were told is 3.0 amps. As the current moves through the loops of the coil, a magnetic field is created in those windings. That magnetic field has energy stored in it. And it’s that energy we want to calculate. The energy in the magnetic field can be thought of as energy stored in the inductor, since the inductor is what’s creating the field.
The energy stored in an inductor is equal to one-half its self-inductance multiplied by the current moving through the inductor squared. We’ve said that the energy in the magnetic field can be equated to the energy of the inductor, that these are one, the same. And so to calculate the energy of the magnetic field, we’ll solve this equation using the given values of the self-inductance for this coil and the current running through it.
The self-inductance of the coil is 5.0 henrys and the current in it is 3.0 amps. If we round our result to two significant figures, we find an answer of 23 joules. That’s the energy stored in this inductor and, therefore, the energy stored in the magnetic field of the inductor.