Electricity and Magnetism

38–252 Electricity and Magnetism

The LHS of the above equation, ε I, is the [instantaneous] power input from the battery into

the RL circuit. The first term on the RHS, I

2

R, is precisely the rate at which energy is

dissipated in the resistor. The remainder of the RHS,

L I

∂I

∂t

=

1

2

L

∂I

2

∂t

= P

M

,

is interpreted as the power being stored in the magnetic field associated with the inductor.

The amount of magnetic energy stored in the inductor, U

M

, may be ascertained by inte-

grating the magnetic power. As the expression for P

M

is a total derivative, the integration

is almost axiomatic:

U

M

=

Z

P

M

dt =

1

2

L I

2

+ “irrelevant constant.”

The constant of integration appearing ...