Problem 20.45 A 34.0-cm long solenoid 1.25 cm in diameter is to produce a field

Question

Problem 20.45

A 34.0-cm long solenoid 1.25 cm in diameter is to produce a field of 4.40 mT at its center.

Part A

How much current should the solenoid carry if it has 960 turns of the wire?

Express your answer using three significant figures and include the appropriate units.

A

Problem 20.45

A 34.0-cm long solenoid 1.25 cm in diameter is to produce a field of 4.40 mT at its center.

Part A

How much current should the solenoid carry if it has 960 turns of the wire?

Express your answer using three significant figures and include the appropriate units.

A

Explanation / Answer

Magnetic field = permeability x turn density x current

B = µ° k * N / L * I
µ° = 4 10^-7
L = 0.34 m --- N = 960 --- N /L = 960 / 0.34 = 2823.529 turns / m
k relative permeability of the core iron k = 200

B = µ° k * N / L * I --- 4.4 x 10-3 = 4 10^-7 * 200 * 2824 * I
I =4.4 x 10-3 / 4 10^-7 * 200 * 2824 = 6.19 x 10-3 = 6.19ma A = 0.00619A

(If k = 1 air I = 0.00619 * 200 = 1.238A)

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