Question

The magnetic field 44.0 cm away from a long, straight wire carrying current 3.00 A is 1360 nT.

(a) At what distance is it 136 nT?
(No Response) cm

(b) At one instant, the two conductors in a long household extension cord carry equal 3.00-A currents in opposite directions. The two wires are 3.00 mm apart. Find the magnetic field 44.0 cm away from the middle of the straight cord, in the plane of the two wires.
(No Response) nT

(c) At what distance is it one-tenth as large?
(No Response) cm

(d) The center wire in a coaxial cable carries current 3.00 A in one direction, and the sheath around it carries current 3.00 A in the opposite direction. What magnetic field does the cable create at points outside the cables?
(No Response) nT

Answer 1

(a)

B = u_oI / 2r

136e-9 = 4e-7 * 3 / 2 * r

2 * r = 4e-7 * 3 / 136e-9

2 * r = 27.719

r = 4.4 m

or

r = 440 cm

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(b)

B_net = u_oI / ( 2R - d) - u_oI / (2R + d)

B_net = 4e-7 * 3 / ( (1 / 0.88 - 0.003) - ( 1 / 0.88 + 0.003))

B_net = 4e-7 * 3 / ( (1 / 0.877) - ( 1 / 0.883))

B_net = 9.297 nT

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c)

now, we want field to be 1/10 of what we found above

so,

1/10 * u_oI / ( 2R - d) - u_oI / (2R + d)

(2R - d) (2R + d) / (2R' - d) ( 2R' + d) = 1/10

where R' is what we are looking for

so,

4R'² = 40R² - 9d²

where R = 44 cm and d = 3 mm

so,

R' = 139.13 cm

____________________

d)

out side the wire

B = 0