Your appropriate electric ion has been instructed to locate a long, straight, ve

Question

Your appropriate electric ion has been instructed to locate a long, straight, vertical current currying wire inside a wall. The wire carries a DC current of I = 13.7 A. The electrician knows that the materials used to controlled the wall do not change the magnetic permeability in his toolbar, the electrician has an campus and as 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? Numeric: A numeric value is expected and not an expression r = ____________ Part (b) The blueprints specify that the current-carrying wire is supposed to be at a depth of r_b = 11.7 cm from the surface of the wall. Calculate the magnetic field strength (in Gauss) at a distance r_b = 11.7 cm from the wire. Numeric: A numeric value is expected and not an expression. B = __________ 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? MultipleChoice: Since the w ire is vertically oriented, the magnetic field generated will not be in a direction detectable with a compass. The compass will only detect magnetic fields generated by wires carrying alternating current. The w ire he is looking for is carrying direct current The magnetic field due to the current is not bigger than that of the earth It is unlikely he will see the slight change in the local magnetic field with a compass. 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? MultipleChoice: The measured magnetic field strength will increase. More information is needed to answer. The measured magnetic field strength will decrease. The measured magnetic field strength will not change as long as the wire is a uniform depth within the wall. Part (e) The electrician measures that the maximum field strength at the surface of the wall is B = 1.23 gauss. Calculate the actual depth of the wire (in cm) from the wall surface. Numeric A numeric value is expected and not an expression. r_a = ____________

Explanation / Answer

Here

I = 13.7 A

part A)

let the distance from the wire is d

B = u0 * I/(2pi * d)

1 *10^-4 = 4pi *10^-7 * 13.7/(2pi * d)

solving for d

d = 0.027 m = 2.74 cm

part b)

at 11.7 cm

magnetic field , B is

B = u0 * I/(2pi * d)

B = 4pi *10^-7 * 13.7/(2pi * 0.117)

B = 2.34 *10^-5 T

part c)

3) at the magnetic field is smaller than earth ,he is unlikely to see the devitation in the compass

part d)

as the magnetic field is constant at constant distance from the wire

the correct option is 4)

part e)

B = u0 * I/(2pi * d)

1.23 *10^-4 = 4pi *10^-7 * 13.7/(2pi * d)

solving for d

d = 0.0222 m = 2.22 cm

the actual depth is 2.22 cm

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