Question

In: Physics

A cube of edge length ℓ = 2.0 cm is positioned as shown in the figure...

A cube of edge length ℓ = 2.0 cm is positioned as shown in the figure below. There is a uniform magnetic field throughout the region with components Bx = +7.0 T, By = +2.0 T, and Bz = +1.0 T.

(a) Calculate the flux through the shaded face of the cube. [Answer] T · m2

(b) What is the net flux emerging from the volume enclosed by the cube (i.e., the net flux through all six faces)? [Answer] T · m2

Solutions

Expert Solution

as the figure is missing in the question so i am calculating the flux for every face of the cube,

A)
Ф = BA cosѲ

→ if the shaded face is perpendicular to the x-axis,
The flux through the shaded side of the cube is found by multiplying the x-component of B perpendicular to the area (A) by the area of the one side (shaded)
Ф_B = B_x * A
(7 T)*(0.02 m)^2 = 0.0028 Tm^2

→ if the shaded face is perpendicular to the y-axis,

The flux through the shaded side of the cube is found by multiplying the y-component of B perpendicular to the area (A) by the area of the one side (shaded)
Ф_B = B_y * A
(2 T)*(0.02 m)^2 = 0.0008 Tm^2

→ if the shaded face is perpendicular to the z-axis,

The flux through the shaded side of the cube is found by multiplying the z-component of B perpendicular to the area (A) by the area of the one side (shaded)
Ф_B = B_z * A
(1 T)*(0.02 m)^2 = 0.0004 Tm^2

B) magnetic field lines form closed loops that have neither a beginning nor an end. So there are not any magnetic field lines inside the cube starting or terminating. The net flux through the cube is zero. Any closed surface will have a net flux of zero.


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