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## Homework Statement

Prove in a current carrying wire the magnetic field only has a theta component.

## Homework Equations

∇ ⋅

**B**= 0 (dive of magnetic field zero, 2nd Maxwell Eq)

∇ x

**B**= μ

**J**(Ampere's Law, 4th Maxwell Eq)

Cylindrical symmetry means B field only dependent on r (distance from z axis) so that

**B**= B

_{r}(r)

**r**hat + B

_{θ}(r)

**θ**hat + B

_{z}(r)

**z**hat

## The Attempt at a Solution

Divergence of Ampere's Law = 0 gives

- ∂B/∂r

**θ**hat + 1/r ∂/∂r(rB

_{θ})

**z**hat = 0

Not really sure where to go from there =/