Your apprentice electrician has been instructed to locate a long, straight, vert

Question

Your apprentice electrician has been instructed to locate a long, straight, vertical, current carrying wire inside a wall. The wire carries a DC current of I = 12.5 A. The electrician knows that the materials used to construct the wall do not change the magnetic permeability, In his toolbox, the electrician has an orienteering compass and a very sensitive magnetic field sensor In this problem, recall that 1 G = 10^-4 T. Part (a) How far from the wire (in cm) would the magnetic field due to the current be exactly 1 Gauss? Part (b) The blueprints specify that the current-carrying wire is supposed to be at a depth of r_b = cm from the surface of the wall. Calculate the magnetic field strength (in Gauss) at a distance r_b = 11.4 cm from the wire. Part (c) The electrician pulls out his orienteering compass to try to locate the wire using the magnetic field from it. As his supervisor why would you recommend that he put his compass back in the toolbox? Part (d) The electrician uses his magnetic field sensor to locate a point on the wall with the strongest magnetic field caused by the current carrying wire. If he moves his sensor up from this spot, what will the reading on his sensor indicate? Part (e) The electrician measures that the maximum field strength at the surface of the wall is B = 1.21 gauss. Calculate the actual depth of the wire (in cm) from the wall surface.

Explanation / Answer

a) R = mu0 * I / (2 pi * B)

= (4 pi * 10-7 * 12.5) / (2 pi * 10-4) = 2.5 cm

b) B = (4 pi * 10-7 * 12.5) / (2 pi * 0.114) = 0.219 G

c) We would recommend him to put his compass back in the tool box because compass will be affected by earth as field will be very small

d) The readings will be same

e) Actual depth = (4 pi * 10-7 * 12.5) / (2 pi * 0.121 * 10-4)

= 20.66 cm

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