What is the magnetic flux?

If the magnetic field caused by a magnet is B=15 webers/meters squared and the field linesgonormally through a Gaussian surface with area A=20cm squared what is the magnetic flux through this surface?

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The definition of magnetic flux is the integral of the magnetic field over a surface area.

F = int_surf ( **B **dot d**S** )

In general, **S** can be any oddly-shaped surface. In your problem statement, all of the flux lines are normal to the surface. This means that you can visualize the answer to the problem by mapping (stretching) the surface into a rectangle shape with surface area 20 cm^2. Just imagine that all the field lines morph with the surface so that they remain normal, and the field density remains 15 W/m^2.

Now, your dealing with a geometry that is simple. B is constant, so take it out of the integral:

F = B int_surf ( **1** dot d**S** ), where **i** is the unit vector normal to the new surface. But, int_surf ( **1** dot d**S** ) is just the area of the surface, 20cm^2.

Thus, F = 20 cm^2 * 15 Web/m^2 * 1 m^2 / ( 100 cm )^2

**F = 30 mWeb**

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