Question

A rigid rectangular loop carrying a current of 5 A is located in the x-y plane with its

four corners at (0, 0), (1 m, 0), (1 m, 2 m), and (0, 2 m). Determine the magnetic
force exerted on each side of the loop if the region in which the loop is located is
permeated with a magnetic field given by

(a) B = 1.5ax T;
(b) B = 1.5az T;

Answer 1

To calculate the magnetic force on a rectangular current-carrying loop in two different magnetic fields, apply the equation ℝF = I (L × B), considering the orientation of the loop and the direction of the magnetic field, using the right hand rule to determine the direction of the force. The net force on the loop is zero, but there may be a net torque.

Step-by-step explanation:

The question involves calculating the magnetic force on a current-carrying loop in a magnetic field, which is a concept in Physics. When a current-carrying conductor is present in a magnetic field, it experiences a force given by the equation ℝF = I (L × B), where ℝF is the force vector, I is the current, L is the length vector of the conductor, and B is the magnetic field vector.

In scenarios (a) and (b), the magnetic field vectors are ⇒B = 1.5⇒ax T and ⇒B = 1.5⇒az T respectively. For each case, one must apply the right hand rule to determine the direction of force on each side of the loop. The forces on opposite sides of the rectangle will be equal and opposite, and hence will not contribute to the net force, but may contribute to a net torque depending on the loop's orientation.

Force Calculation for Case (a)

For case (a), the sides along the y-axis will experience no force because the magnetic field is aligned with the x-axis (i.e., there is no component of the field perpendicular to the current direction on these sides). For the sides parallel to the x-axis, the forces will be equal and opposite, and their magnitudes can be calculated using the cross-product of the current carrying segment and the magnetic field: F = I * L * B; where L is the length of the side and B is the magnetic field's magnitude.

Force Calculation for Case (b)

For case (b), the magnetic field is aligned with the z-axis, so the forces on all sides of the loop will be perpendicular to both the direction of the current and the magnetic field. Again, the forces on opposite sides will be equal in magnitude and opposite in direction, resulting in a net force of zero but possibly producing a net torque depending on the loop's orientation.