1 answer

Magnetic Fields due to Currents in 4 wires

Question:

Four long straight wires are perpendicular to the page, and their cross sections form a square of edge length a=26cm. The currents are out of the page in wires 1and 4 and into the page in wires 2 and 3, and each wire carries 24A. What is the magnitude of the net magnetic field at the square's center?


Answers

We'll use Biot-Sevart law:

and in our case:

B*2πr=μ0*I

r is the distance between each wire and the canter of the square being equal to sqrt(132+132)=13*sqrt(2) and I being the current.

so we get:

B=μ0*24/(2*0.26π)=600μ0/13π

This is the magnetic field each wire generates. the direction is according to the right hand rule.

so if the qires are positioned:

1 2

3 4

Then the magnetic field in the midle is zero since 1 and 4 cancel each pther out and 2 and 3 also cancel out.

If the wires are:

1 2

4 3

then the magnetic field is 4*B=2400μ0/13π and the direction is from the center toward wire number 4.

.

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