Question

A 0.166 m x 0.392 m rectangular loop of wire is placed in a uniform 0.747 Tesla magnetic field that points in the +y direction. The the wire loop initially lies in the x-z plane and the center of the loop is at x=0, y=0, z=0. What is the change in magnetic flux through the loop in SI units if the loop is then rotated by 24.5 degrees about the z axis? Express the answer as a positive or negative number.

Answer 1

To calculate the change in magnetic flux through the loop, use the equation Δφ = BΔAcosΘ. The change in area can be calculated by multiplying the initial area of the loop by sin(24.5°). Finally, calculate the change in magnetic flux by multiplying the magnetic field strength, change in area, and cos(24.5°).

Step-by-step explanation:

The change in magnetic flux through a loop can be calculated using the equation Δφ = BΔAcosΘ, where φ is the magnetic flux, B is the magnetic field strength, ΔA is the change in the area, and Θ is the angle between the magnetic field and the normal to the loop's surface. In this case, the initial area of the loop is given by A = 0.166 m x 0.392 m = 0.065152 m². The change in area when the loop is rotated by 24.5 degrees about the z-axis can be calculated as ΔA = 0.065152 m² x sin(24.5°). Using the given magnetic field strength, the change in magnetic flux through the loop can be calculated as Δφ = 0.747 Tesla x 0.065152 m² x cos(24.5°). The result will be a positive or negative number depending on the direction of the rotation.