Question

The magnetic field 38.0 cm away from a long, straight wire carrying current 4.00 A is 2110 nT.

(a) At what distance is it 211 nT?

380 cm

(b) At one instant, the two conductors in a long household extension cord carry equal 4.00-A currents in opposite directions. The two wires are 3.00 mm apart. Find the magnetic field 38.0 cm away from the middle of the straight cord, in the plane of the two wires.

16.6 nT

(c) At what distance is it one-tenth as large?

_______________________cm

(d) The center wire in a coaxial cable carries current 4.00 A in one direction, and the sheath around it carries current 4.00 A in the opposite direction. What magnetic field does the cable create at points outside the cables?
0 nT

Answer 1

As I can see you only need help with part C, If you need help with any other part A, or D comment below.

Part B.

Magnetic field due to current carrying wire is given by:

B = u0*i/(2*pi*r)

Now since current is in opposite direction, So net magnetic field 39.0 cm away from the middle of the cord will be

Bnet = B1 - B2

Bnet = u0*i/(2*pi*r1) - u0*i/(2*pi*r2)

Bnet = (u0*i/(2*pi))*(1/r1 - 1/r2)

i = current in wires = 4.00 Amp

Since distance between both wires is 3.00 mm = 0.3 cm, So from the middle of the cord

r1 = distance from cord center to field point due to wire 1 = 38 cm - 0.3 cm/2 = 37.85 cm = 0.3785 m

r2 = distance from cord center to field point due to wire 2 = 38 cm + 0.3 cm/2 = 38.15 cm = 0.3815 m

So,

Bnet = (4*pi*10^-7*4.00/(2*pi))*(1/0.3785 - 1/0.3815)

Bnet = 16.6*10^-9 T

Bnet = 16.6 nT

Part C.

At what distance magnetic field is one-tenth as large

Bnet = 16.6 nT (from part (b))

So one-tenth, B1net = 16.6/10 = 1.66 nT

Now Suppose at distance r, net magnetic field is 1.66 nT, then

B1net = B1 - B2

B1net = (u0*i/(2*pi))*(1/r1 - 1/r2)

r1 = r - d, and r2 = r + d

d = distance of wires from center of cord = 3.00 mm/2 = 1.5 mm = 0.0015 m

So,

B1net = (u0*i/(2*pi))*(1/(r - d) - 1/(r + d))

B1net = (u0*i/(2*pi))*(2d/(r^2 - d^2))

r^2 - d^2 = u0*i*d/(pi*B1net)

r^2 = d^2 + u0*i*d/(pi*B1net)

Using known values:

r^2 = 0.0015^2 + (4*pi*10^-7*4.00*0.0015/(pi*1.66*10^-9))

r^2 = 1.445785

r = sqrt (1.445785)

r = 1.202 m

r = 120.2 cm

Please Upvote.

Comment below if you've any query.