Two parallel conductors carry currents in opposite direction

Two parallel conductors carry currents in opposite directions, as shown in Figure P19.56. One conductor carries current of 10.0 A. Point A is the midpoint between 2 wires, and point C is 5.00 cm to the right of the 10 D A current I is adjusted to that the magnetic field at C zero. Find the value of the current I and the value the magnetic field at A.

Solution

a) The magnetic field decreases proportionally to the distance increase. At point C, the first conductor is 5 cm away while the second conductor is 15cm away (3x farther)

So the current in the second conductor has to be -3 time stronger to counteract the effect of the first one.

so -3x10.0 = -30 A or 30 A in the opposite direction.

b) The magnetic field from long straight current carrying wire is

B = (0 * I) / (2 * * A) where
I is current intensity
A is distance
0 is the permeability constant = 4*10^7 N/A^2

B = 2*10^-7 * I/A Teslas

At A the magnetic field will be the sum of B1 and B2 where

B1 = 2E-7 * 10/(5E-2) and
B2 = 2E-7 * -30/(5E-2)

B = 2E-7 * -20/5E-2 = 8E-5 Teslas = 0.00008 T