Question

Two straight parallel wires are separated by 7.1 cm . There is a 2.0-A current flowing in the first wire.

Part A

If the magnetic field strength is found to be zero between the two wires at a distance of 2.1 cmfrom the first wire, what is the magnitude of the current in the second wire?

Express your answer using two significant figures and include the appropriate units.

Part B

What is the direction of the current in the second wire?

A: direction opposite to the current in the first wire

B: same direction as the other current

Answer 1

(a) magnetic field due to straight long conductor is given by B = uo i/(2 pi r)

magnetic field due to first conductor at r= 2.1 cm is given by

B= (4 pi x10^-7 )*2 /( 2* pi * 0.021)

B=1.9x10^-5 T

now the total magnetic field =0 . so the magnetic field due to the other conductor has to be in opposite direction to that of the original magnetic field and equal in magnitude so that the two magnetic fields add up to produe total of zero

so magnetic field due to second conductor= 1.9x106-5 T

r= 7.1- 2.1= 5 cm = 0.05 m

uo i/(2 pi r) = 1.9x10^-5

(4 pi x10^-7 )*i /( 2* pi * 0.05) =1.9x10^-5

4x10^-6 i= 1.9x10^-5

i= 1.9x10^-5 /(4x10^-6)

i= 4.75 A

(b) for direction of current, we have to use the right hand rule. Using the right hand rule we can see that for the magnetic fields to be in opposite direction between the two wires(so that total field is zero), the current must be flowing in the same direction as that of the first wire.