Question

Two long, straight wires are separated by 0.12 m. The wires carry currents of 4.0 A in opposite directions, as the drawing indicates. Find the magnitude of the net magnetic field at the point A.
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https://general.physics.rutgers.edu/gifs/CJ/21-12.gif

Answer 1

Use ampere's law and the right hand grip rule.

Ampere's law:
\[\oint Bdl=\mu_{0}I_{encl}\]In this case, the B field for a single current carrying conductor is simply
\[B=\frac{\mu_{0}I_{encl}}{2\pi R}\]

I temporary remove the top loop first. The bottom loop has a R of 0.15m and the direction of the field using the right hand grip rule is downwards.

Then i temporary remove the bottom loop. In this case the R is 0.03m and the direction of the field at A using the right hang grip rule is upwards.

Taking upwards as positive,
\[B_{net}=\frac{4\mu_{0}}{2\pi}(\frac{1}{0.03}-\frac{1}{0.15})\]