The four wires that lie at the corners of a square of side a= 4.80 cm are carryi

Question

The four wires that lie at the corners of a square of side a= 4.80 cm are carrying equal currents i= 1.00 A into (+) or out of (-) the page, as shown in the picture.

1.Calculate the y component of the magnetic field at the center of the square.

2.Calculate the x-component of the force on a 1.0-cm long piece of the lower right-hand wire, due to the other three wires.

Please show all work!

The four wires that lie at the corners of a square of side a= 4.80 cm are carrying equal currents i= 1.00 A into (+) or out of (-) the page, as shown in the picture. 1.Calculate the y component of the magnetic field at the center of the square. 2.Calculate the x-component of the force on a 1.0-cm long piece of the lower right-hand wire, due to the other three wires.

Explanation / Answer

Probably, the problem requires the total magnetic field in the origin. It is null since the pair of wires with y>0 generate a field directed upward, while, the wires with y<0 generate a total field directed downward. Since the currents carried by all the wires and their distances are equal, the magnitude of the fields is identical.

The basic Biot-Savart law for the magnetic field of a wire is used. Recall the right-hand rule when you compute the vector product

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