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The electric field

**E**is more or less 1D so it is unchanged. In N dimensions there is no such thing as a magnetic pole, so one needs to return to basic special relativity to see what will happen. Magnetism is 2D: the remainder of dimensions are irrelevant. It's plane is defined by three points: the location of the source charge, the location of the source charge after dt, and the location of the affected particle. Magnetism can be represented by a bivector

**B**which defines the plane in which magnetism operates, the magnitude, and the sign. The magnetic force is calculated by taking the inner product of B with the velocity vector of a charged particle. The inner product of a vector with a bivector is the projection of that vector onto the plane rotated 90 degrees, which just so happens to be precisely what we want.

A scalar is grade zero, an ordinary monovector is grade 1, a bivector is grade 2, etc.

In GA gradient = div + curl. Taking the div lowers the grade while the curl increases the grade. Take the time derivative leaves the grade unchanged.

Everything is as usual with the monovector

**E**. Field

**B**is the curl of the charge current potential vector, so it is a bivector. The divergence of a bivector is a vector, while the curl is a trivector. There are no trivector terms on the other side of the equation, so it must be zero.

With no charges,

div E = 0

curl E = -dB/dt

div B = -dE/dt

curl B = 0

The grade of both sides of each of the equations is, in order,

0

2

1

3

That's all there is to it, for any N dimensions.