Question

The two 10-cm-long parallel wires in the figure are separated by 5.0 mm. For what value of the resistor R will the force between the two wires be 9.00×10−5 N?

Answer 1

To find the value of the resistor R that will result in a force between the two parallel wires, we need to calculate the magnitude and direction of the force using the formula F = (μm0I1I2)/2πr. Plugging in the given values, we can solve for R.

Step-by-step explanation:

To find the value of the resistor R that will result in a force between the two parallel wires, we need to calculate the magnitude and direction of the force first.

Part (a):

When the currents in the wires flow in opposite directions, the magnitude of the force per unit length (F) can be calculated using the formula:

F = (μm0I1I2)/2πr

Where μm0 is the permeability of free space (4π × 10-7 Tm/A), I1 and I2 are the currents in the wires, and r is the distance between the wires.

Plugging in the given values, we can solve for R.

Part (b):

When the currents in the wires flow in the same direction, the magnitude of the force per unit length can be calculated using the same formula. The only difference is the direction of the force will be reversed.

Answer 2

To calculate the force between two parallel wires, you can use Ampere's Law. By rearranging the formula, you can find the value of R that will produce a certain force.

Step-by-step explanation:

To calculate the force between two parallel wires, you can use Ampere's Law. When the currents flow in opposite directions, the force per unit length is given by:

Force per unit length = (μ0 × I1 × I2) / (2πd)

Where μ0 is the permeability of free space (4π × 10^-7 T·m/A), I1 and I2 are the currents in the wires, and d is the separation between the wires. By rearranging the formula, you can find the value of R that will produce a force of 9.00×10^-5 N.