## Mastering Physics Solutions: Exercise 19.45

Exercise 19.45

Part A = to the right
Part B = 0.063 T

Solutions Below:

A solenoid is wound with 250 turns per centimeter. An outer layer of insulated wire with 200 turns per centimeter is wound over the solenoid’s first layer of wire. When the solenoid is operating, the inner coil carries a current of 10 A and the outer coil carries a current of 15 A in the direction opposite to that of the current in the inner coil.

Part A

What is the direction of the magnetic field at the center for this configuration?

The magnetic field in a solenoid is:

B = μ0 * I * n

Where μ0 is the magnetic constant, I is the current, and n is the number of coils per meter.

Since the solenoid in this problem has two layers, find the larger of the two magnetic fields and just use the right hand rule to determine the direction. See Part B for more info.

to the right

Part B

What is the magnitude of the magnetic field at the center of the doubly wound solenoid?

The magnetic field in a solenoid is:

B = μ0 * I * n

Where μ0 is the magnetic constant, I is the current, and n is the number of coils per meter. Since the solenoid in this problem has two layers, just take the difference, which will give you the magnitude of the magnetic field.

Find the magnetic field from the inner layer:

Binner = 1.2566*10^-6 * 10 * 25000
Binner = 0.31415

Now find the magnetic field from the outer layer:

Bouter = 1.2566*10^-6 * 15 * 20000
Bouter = 0.37698

Take the difference to find the overall magnetic field:

0.063 T

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