Question

A uniform magnetic field of 4.15 T points in some direction. Consider the magnetic flux through a large triangular wire loop that has three equal sides of 1.65 m. Determine the maximum of the absolute value of the magnetic flux.

Answer 1

ФB = 4.89 W

Step-by-step explanation:

In order to calculate the magnetic flux trough the triangular wire loop, you use the following formula:

`\Phi_B=B\cdot A=BAcos\theta` (1)

B: magnitude of the magnetic field = 4.15T

A: area of the triangular loop

θ: angle between the normal to the surface and the direction of the magnetic field = 0°

Both direction of the magnetic field and the normal vector to the surface are parallel.

You calculate the area of the triangular loop:

`A=(bh)/(2)` (2)

b: base = 1.65 m

h: height =
`\sqrt{(1.65m)^2-((1.65m)/(2))^2}=1.42m`

`A=((1.65m)(1.42m))/(2)=1.17m^2`

Next, you replace the values of A and B in the equation (1):

`\Phi_B=(4.15T)(1.17m^2)=4.89W`

The magnetic flux trough the triangular wire loop is 4.89W