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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.

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

Added Mon, 03 Aug '15

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