Question

A long pair of insulated wires serves to conduct 54.0 A of dc current to and from an instrument.

If the wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.0 cm from their midpoint, in their plane (see the figure(Figure 1) )?

Express your answer using two significant figures.

Compare to the magnetic field of the Earth (5.0×10−5T).

Express your answer using two significant figures

Answer 1

answer: From ampere's law ∫B*dl = µ0*I. For a line of current, B is uniform around I so ∫B*dl = 2*π*r*B, where r is the distance from the wire. Then

B = µ0*I/(2*π*r)

There are two wires and the fields will sum. However, the currents are going in opposite direction,

B = µ0*I/(2*π) * (1/r1 - 1/r2).

µ0 = 4*π*10^-7 T*m/A

B = 2*10^-7*I*(1/r1 - 1/r2)

r1 = .0986 m
r2 = .1014 m

B = 2*28*(1/,0986 - I/.1014)*10^-7 T = 1.57*10^-6 T

#comparing with earths magnetic field:-------

The strength of the field at the Earth's surface ranges from less than 30 microteslas (0.3 gauss) in an area including most of South America and South Africa to over 60 microteslas (0.6 gauss) around the magnetic poles in northern Canada and south of Australia, and in part of Siberia.