A right triangular prism lies on its side in a horizontal magnetic field of 3.72

Question

A right triangular prism lies on its side in a horizontal magnetic field of 3.72T in the x direction. The triangle has a base (in the x direction) of 0.347m , and height (in the y direction) of 0.614m . The height of the prism (in the z direction) is 1.211m .(Figure 1)

Part A

What is the magnetic flux through the side of the prism's bottom? (This is on the zx plane where y = 0.)

Part B

What is the magnetic flux through the side of the prism's front? (This is on the xy plane where z = 1.211m .)

Part C

What is the magnetic flux through the side of the prism's back? (This is on the xy plane where z = 0.)

Part D

What is the magnetic flux through the side of the prism's left? (This is on the zy plane where x = 0.)

Part E

What is the magnetic flux through the side of the prism's right? (At an angle)

Explanation / Answer

Magnetic flux = B*s*cos(theta)

where B, s and theta are magnetic field, surface area and angle between field and area vector respectively.

(a) Area vector is perpendicular to the area. So, area vector is in y-direction.

Angle between B and s = 90 degrees.

Since cos(90) = 0,

flux = 0

(b) Length of hypotenuse = sqrt(0.347^2 + 0.614^2) = 0.705 m

So, area, s = 1.211*0.705 = 0.854 m^2

Angle between area vector and x-axis is same as angle between the face and y-z plane.

So, cos(theta) = 0.614/0.705 = 0.871

So, flux = 3.72 * 0.854*0.871 = 2.76 T

(c) Area vector is x-axis. So, cos(theta) = 1, as theta = 0

Area = 0.614*1.211 = 0.744 m^2

Flux = 3.72*0.744 = 2.76 T

(D) and (E) area vector is z-axis. Angle between area vector and B = 90 degrees.

So, cos(theta) = 0

So, flux = 0

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