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Magnetic Field Due to a Straight Current Carrying Conductor

Find the magn...

Question

Find the magnetic field strength B of an infinite plane carrying a current of linear density J (small at all points).

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Solution

Applying Ampere Circuital Law in the loop:
$\int B \cdot d l = μ_{0} J (l)$
$⟹ B (2 l) = μ_{0} J l$
$⟹$ $B = \frac{μ_{0} J}{2}$
The magnetic field intensity is horizontal and parallel to the plane.

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