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Two long, parallel wires separated by 30cm each carry currents of 2.0A in a horizontal direction. A) Find the magnetic field midway between the wires if the currents are in the same direction. B) Find if they are in opposite directions.
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Added Mon, 03 Aug '15
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For a current carrying wire of infinite length , the magnetic field lines are concentric circles
in planes prependicular to the wire.
� The magnitude of the magnetic field at distance R from the center of the wire is B = (u * I ) / (2 * (pi) * R) .

where u = magnetic permeability of Free Space = 4 * (pi) * 10^(-7) ,

I = current through the wire.

R = distance between the wire and the point where field has to be calculated .

a) Therefore for I = 2 Amps , R = 15 cm ,(midway)

Magnetic Field due to first wire B1 = (u * I ) / (2 * (pi) * R) = 2.667 * 10^(-6) Tesla .

Magnetic Field due to first wire B2 = (u * I ) / (2 * (pi) * R) = 2.667 * 10^(-6) Tesla .

Since, both currents are in same direction, acccording to "Right hand Rule", they cancel out each other .

The net Magnetic Field due to both the wires B = (2.667 * 10^(-6)) - (2.667 * 10^(-6)) = 0 Tesla.

b) For both currents in opposite direction, they add up.

So, the net Magnetic Field due to both the wires B = (2.667 * 10^(-6)) + (2.667 * 10^(-6)) = 5.33 * 10^(-6) Tesla.

Reference : http://www.phys.uri.edu/~gerhard/PHY204/tsl216.pdf
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