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Q.34

Expert-verified
Found in: Page 832

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

The two 10-cm-long parallel wires in FIGURE EX29.34 are separated by 5.0 mm. For what value of the resistor R will the force between the two wires be 5.4 * 10-5 N?

See the step by step solution

Part 1 : Given Information

Two current -carrying wires generate forces between them since ordinary currents produce magnetic fields and this fields exert significant forces on ordinary currents. The forces on the wires re equal in magnitude and it is given by equation (29.27) in the form

where d is the distance between the two wires and is the length of the wire were both wires have the same length, The force is attractive if the current are in the same direction and repulsive if they are in opposite directions.

We can assume that the current in the left circuit is , so we use Ohms law to get this current as Ohm's law states that the current flows through a resistance due to the potential difference between the resistance.

let us determine the current through the left wire using the values for and of the battery by

We rearrange equation(1) for to be in the form

Part 2 : calculation

Where is the current in right wire. Now, plug the values for into equation(3) to get

Again we use the Ohms law to get the resistance in the right circuit by using the value of the potential difference .