Flux through a small element of thickness, dx is:

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

A magnetic field is given by *B*⃗ =*B*_{0}(*x*/*x*_{0})^{2}*k *, where *B*_{0} and *x*_{0} are constants.

Find an expression for the magnetic flux through a square of side 2*x*_{0} 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 *B*_{0} and *x*_{0}.

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