Q. 79

Expert-verifiedFound in: Page 835

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

You have a 1.0-m-long copper wire. You want to make an N-turn current loop that generates a 1.0 mT magnetic field at the center when the current is 1.0 A. You must use the entire wire. What will be the diameter of your coil?

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The total length of the copper wire is , the current through the wire is and the magnetic field at the center of the coil is .

The formula to calculate the total length of the wire can be written as

Here, is the total length of the wire, i the number of turns when the wire is bent into a circular loop and is the diameter of the loop.

Simplify equation (1) to obtain the number of turns in the loop.

The formula to calculate the magnetic field at the center of a circular loop is given by

Here, is the magnetic field, is the permeability of free space and is the current through the loop.

Substitute the expression for the number of turns from equation (2) into equation (3) and simplify to obtain the diameter of the loop.

Substitute for , for , for and for into equation (4) to calculate the required diameter.

The required diameter of the loop is .

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