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applestrudle
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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 = Br(r)rhat + Bθ(r)θhat + Bz(r)zhat
The Attempt at a Solution
Divergence of Ampere's Law = 0 gives
- ∂B/∂r θhat + 1/r ∂/∂r(rBθ) zhat = 0
Not really sure where to go from there =/