Question

Two flat surfaces are exposed to a uniform, horizontal magnetic field of magnitude 0.80 T. When viewed edge-on, the first surface is tilted at an angle of 20° from the horizontal, and a net magnetic flux of 8.3 x 10^-4 Wb passes through it. The same net magnetic flux passes through the second surface. (a) Determine the area of the first surface. (b) Find the smallest possible value of the area of the second surface.

Answer 1

Given

uniform horizontal magnetic field is B = 0.80 T

the angle of the first surface tilted from the horizontal is 20 degrees

from definition of magnetic flux phi = B*A cos theta

theta is the angle between the magnetic field and normal to the surface  

given flux is phi_1 = 8.3*10^-4 Wb

a) area of the first surface is A = phi_1/(Bcos theta)

A1 = 8.3*10^-4 /(0.8 cos20) m^2

A1 = 0.0011041 m^2

b) the values of the second suface area is  

A2 = phi_1/(B1*cos 0)

if the second surface is along y axis if the magnetic field is along x axis

A2 = 8.3*10^-4/(0.8*1) m^2

A2 = 0.0010375 m^2