Two long straight current-carrying parallel wires cross the x axis and carry currents I and 3I in the same direction, as shown. At what value of x is the net magnetic field zero?
A) 0
B) 1
C) 3
D) 5
E) 7

Question

Two long straight current-carrying parallel wires cross the x axis and carry currents I and 3I in the same direction, as shown. At what value of x is the net magnetic field zero? 
A) 0 
B) 1 
C) 3 
D) 5 
E) 7

Quizplus · Accepted Answer

The magnetic field produced by a wire carrying current I at a distance r from the wire is given by:
$B = \frac{\mu_0 I}{2\pi r}$, where $\mu_0$ is the permeability of free space.
For wire carrying current 3I, the magnetic field produced at distance r is:
$B' = \frac{\mu_0 (3I)}{2\pi r} = 3\frac{\mu_0 I}{2\pi r} = 3B$
At any point on the x axis, the magnetic field due to the wire carrying current I is in the opposite direction to the magnetic field due to the wire carrying current 3I, so the net magnetic field is given by:
$B_{net} = B - B' = B - 3B = -2B$
For the net magnetic field to be zero, we need $B=0$, which occurs when $x=3$. Therefore, the answer is C.

Two Long Straight Current-Carrying Parallel Wires Cross the X Axis