Question

Two coils which are close together have a mutual inductance of 330mH if the emf in coil #1 is 120V, what is the rate of change of the current in coil #2?

a)If the current of change of coil # current in coil #1 is 36A/sec, what is the emf in coil #2

b)If the current in a 280mH coil changes steadily from 25.0 A to 10.0 A in 360ms, what is the magnitude of the induced emf?

c) What is the energy density at the center of a circular loop of wire carrying 23.0 A current if the radius of the loop is 28.0cm?

Answer 1

When 2 coils are next to each other, a changing current through one will cause an emf to develop in the other, given by:

a) Now a changing current in coil 1 induces an emf in coil 2:

b) The induced emf in a coil by self inductance is:

Note that 10 A is the final value and 25 A is the initial value for current.

c) A loop of wire carrying current generates a magnetic field, and a region of space where magnetic field lies contains energy density given by:

The magnetic field at the center of a loop can be calculated using Biot Savart's Law:

Knowing that B is normal to the plane of the loop and that the length vector dl an the position vector r are allways perpendicular to each other along the circular path:

The sumation of all the lengths is just the circumference of the circle, then:

Replacing with the given values:

So finally