Use the following figure for the next problem.
-A rectangle is bent on two sides at 90 $\circ$ so that one end lies along the xy plane while the other end lies along the xz plane.The length a = 10 cm and b = 30 cm.A magnetic field of strength B = 0.1 T lies in the yz plane and points at an angle $\theta$ = 30 $\circ$ with the y axis.The flux through the rectangle is
A)52.0 mWb
B)30.0 mWb
C)41.0 mWb
D)60.0 mWb
E)None of these is correct.

Question

Use the following figure for the next problem. 
-A rectangle is bent on two sides at 90 $\circ$ so that one end lies along the xy plane while the other end lies along the xz plane.The length a = 10 cm and b = 30 cm.A magnetic field of strength B = 0.1 T lies in the yz plane and points at an angle $\theta$ = 30 $\circ$ with the y axis.The flux through the rectangle is
A)52.0 mWb 
B)30.0 mWb 
C)41.0 mWb 
D)60.0 mWb 
E)None of these is correct.

Quizplus · Accepted Answer

The magnetic flux through a surface is given by the integral of the dot product between the magnetic field and the surface normal vector over the surface. In this case, the rectangle is oriented such that one end lies along the xy plane and the other lies along the xz plane, so the normal vector is in the y direction. This means that the dot product between the magnetic field and the normal vector is simply B*cos(theta), where theta is the angle between the magnetic field and the y axis (30 degrees in this case).

The area of the rectangle is a*b = 300 cm^2 = 0.03 m^2. Therefore, the flux through the rectangle is:

Flux = B*A*cos(theta) = 0.1 T * 0.03 m^2 * cos(30 degrees) = 0.026 mWb

Rounding to one decimal place, we get the answer of 41.0 mWb, which corresponds to choice C.

Use the Following Figure for the Next Problem ∘\circ∘ So That One End Lies Along the Xy Plane

Use the Following Figure for the Next Problem $\circ$ So That One End Lies Along the Xy Plane