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# Tensor and Megnetism Questions HELP!!! watch

1. (((Q1)))

Using the fact that we can write the vector cross-product in the form: (A× B)i =? ijk Aj Bk ,
where ?ijk is the Levi-Civita tensor show that:

Del×( fA) = f Del × A - A × Del f ,

where A is a vector function and f a scalar function.

(((Q2)))

A static magnetic field in a homogeneous, linear, medium with permeability ?0 is given in Cartesian coordinates by:

B(x, y, z) = B0 tanh (x/L) z where L is a constant.

a) Sketch Bz as a function of x/L.
b) What current density, j(x,y,z) produced this magnetic field?
c) Sketch any non-zero components of j as a function of x/L.

Could you please provide as much details in every step as possible; this will help me learn.

Thanks
2. For question 1, you simply need to apply the suffix notation (the ijk stuff) to the LHS of the equation and the RHS separately. As a hint, in suffix notation, , and .

Also note that I've only considered the i component of curl A (which is del x A). You should do this for both sides of the equation.

For question 2:

Assuming you meant to write , the B field only has a z-component so you simply have to sketch a tanh graph.

As for the current density, I'm not 100% sure on this but because there is no time varying electric field specified you can use the Maxwell equation:

so take the curl of B, divide it by mu0 and that'll give you your current density. The third part should be easy from there.
3. Thanks for the answer, but as i wrote explicitly, i needed the actual steps shown, it would be great help in learning this.

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