If Div B = 0, where B = magnetic field

Blaine Stein

Blaine Stein

Answered question

2022-05-13

If Div B = 0, where B = magnetic field intensity, then B must be a Curl of a some vector function. What is that vector function?

Answer & Explanation

Abigailf91er

Abigailf91er

Beginner2022-05-14Added 13 answers

It is called the electromagnetic vector potential, A(r,t)
B ( r , t ) = × A ( r , t )
where the operator, ×, is the curl. The electric field has also a part derived from it, as follows:
E ( r , t ) = ϕ ( r , t ) A ( r , t ) t
where ϕ ( r , t ) is the scalar potential.
These two definitions arise from the Maxwell equations, however, A and ϕ are not unique, they can always be shifted by a continuous function, χ ( r , t ), such that, transforming
A ( r , t ) A ( r , t ) + χ ( r , t ) ϕ ( r , t ) ϕ ( r , t ) χ ( r , t ) t
will also satisfy the Maxwell equations. This is called gauge transformation.

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