Exercise 26.39 Number 12 gauge wire, commonly used in household wiring, is 2.053

ID: 1435386 • Letter: E

Question

Exercise 26.39

Number 12 gauge wire, commonly used in household wiring, is 2.053 mm in diameter and can safely carry currents of up to 20.0 A.

Part A: For a wire carrying this maximum current, find the magnetic field strength 0.130 mm from the wire's axis. Answer in T:

Part B: For a wire carrying this maximum current, find the magnetic field strength at the wire's surface. Answer in T:

Part C: For a wire carrying this maximum current, find the magnetic field strength 0.365 mm beyond the wire's surface. Answer in T:

When answering the question, could you please make it clear which of the equations you are using to solve the problem? Thank you.

given

radius R = d/2 = 2.053/2 mm = 1.0265 mm

R = 1.0265 * 10^-3 m

current I = 20 A

part A

inside the wire magnetic field is given by

B = mue not * I * r / 2pi * R^2

B = (4pi * 10^-7 * 20 * 0.13 * 10^-3) / (2pi * sqr(1.0265 * 10^-3))

B = 4.9 * 10^-4 T

part B

on the surface (r = R)

B = mue not * I / 2pi * R

B = (4pi * 10^-7 * 20 / (2pi * 1.0265 * 10^-3)

B = 38.97 * 10 ^-4 T

part C

outside the wire

B = mue not * I / 2pi * r

r = 1.0265 + 0.365 = 1.3915 mm

B = (4pi * 10^-7 * 20 / (2pi * 1.3915 * 10^-3)

B = 28.74 * 10^-4 T

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