A battery is connected to a Nichrome wire and a conventional current of 0.5 ampe

Question

A battery is connected to a Nichrome wire and a conventional current of 0.5 ampere runs through the wire. The wire is laid out in the form of a rectangle 50 cm by 2.5 millimeters. (a) What is the magnetic field at the center of the rectangle due to the current in the wire? (The +x axis points to the right, the +y axis points up and the +z axis points out. The current is running clockwise.) (b) What approximations did you make? The wire is sufficiently long to be able to use B = (mu_0/4pi)2I/r. The effect of the distant vertical wires is negligible. The electron mobility in the wire is very high. The width is sufficiently narrow that r length of wire.

Explanation / Answer

approximations are correct.and accordingly field at centre

B = 2 x (u0I/(2 x pi x r)) r = 2.5/2 mm = 1.25 x 10-3 m, u0 = 4 x pi x 10-7

B = 4 x 10-7 x 0.5/( 1.25 x 10-3) = 1.6 x 10-4 T

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