Question

The magnetic field 39.0 cm away from a long, straight wire carrying current 4.00 A is 2050 nT.

(a) At what distance is it 205 nT?
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 39.0 cm away from the middle of the straight cord, in the plane of the two wires.
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?
nT

Answer 1

a)

Magnetic field at a distance from a straight current carrying conductor is

At two points magnetic fields are ,    

At , ,

b)

The two wires are at a distance

Magnetic field at a distance from the middle of straight cord ( in the plane of two wires) due to two wires is

( the two currents in opposite directions )

c)

Approximating above equation,

For ,

For ,  

d)

Ampere's law

Charge enclosed in the Amperean loop is ( since the currents in wire and sheath around wire are in opposite directions )

Hence magnetic field outside the cables is