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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A long solenoid that has 1.00 × 103 turns uniformly distributed over a length of 0.400 m produces a magnetic field of magnitude 1.00 × 10−4 T at its center. What current is required in the windings for that to occur?

To determine

The current carried by the windings.

Explanation

Given info: The number of turns in the wire is 1.00×103. The length of the solenoid is 0.400m. The magnetic field at the center of the solenoid is 1.00×104T.

The magnetic field inside a solenoid is given by,

B=μ0nI      (1)

  • μ0 is the permeability of free space
  • I is the current
  • n is the number of turns per unit length

The number of turns per unit length can be written as,

n=Nl      (2)

  • N is the total number of turns
  • l is the length of the solenoid

From (1) and (2),

B=μ0(Nl)I

On re-arrangement,

I=Blμ0N

Substitute 4π×107TmA-1 for μ0, 1

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