Magnetic Flux with Calculus Video Lessons

Concept

# Problem: A magnetic field is given by B⃗ =B0(x/x0)2k , where B0 and x0 are constants.Find an expression for the magnetic flux through a square of side 2x0 that lies in the x-y plane with one corner at the origin and two sides coinciding with the positive x and y axes.Express your answer in terms of the variables B0 and x0.

###### FREE Expert Solution

Flux through a small element of thickness, dx is:

$\overline{){\mathbf{d}}{\mathbf{\varphi }}{\mathbf{=}}\stackrel{\mathbf{⇀}}{\mathbf{B}}{\mathbf{.}}{\mathbf{d}}\stackrel{\mathbf{⇀}}{\mathbf{A}}}$

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###### Problem Details

A magnetic field is given by B⃗ =B0(x/x0)2, where B0 and x0 are constants.

Find an expression for the magnetic flux through a square of side 2x0 that lies in the x-y plane with one corner at the origin and two sides coinciding with the positive x and y axes.