A rectangle is bent on two sides at 90º 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 Ɵ = 30º 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

A rectangle is bent on two sides at 90º 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 Ɵ = 30º 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 area of the rectangle projected onto the yz plane is A = b*h = 30*h, where h is the height of the rectangle. The component of the magnetic field perpendicular to this area is B*sin(Ɵ) = 0.1*sin(30º) = 0.05 T. Thus, the flux through this area is Φ = B*A*cos(Ɵ) = 0.05*30*h*cos(30º) = 0.75*h mWb. To find h, we note that the sides of the rectangle are bent at right angles, so the height of the rectangle in the xy plane is h*cos(30º) = a*cos(60º) = 5 cm. Therefore, the flux through the rectangle is Φ = 0.75*5 = 3.75 mWb, or 41.0 mWb to two significant figures. The correct answer is therefore (C).

A Rectangle Is Bent on Two Sides at 90º So