Along wire carrying a 6.0 a current perpendicular to the xy-plane intersects the x-axis at x=−2.3cm. a second, parallel wire carrying a 3.0 a current intersects the x-axis at x=+2.3cm. (part a) at what point on the x-axis is the magnetic field zero if the two currents are in the same direction? (part b) at what point on the x-axis is the magnetic field zero if the two currents are in opposite directions?

a) X = 0.767cm

b) X = 6.9cm

Explanation:

If both currents are in the same direction, the point of magnetic field zero must be somewhere in between the two wires. In this case, we have:

  Since both magnetic fields must be equal in order cancel each other, and assuming that the point is closer to the 3A wire:

 where would be the factor to convert the distances from cm to m.

If we solve the equation for x, we get:

x = 0.767cm

Now, if both currents are in opposite direction, the point of magnetic field zero would be outside of the two wires and closer to the 3A wire. The formulas for this scenario would be:

   where would be the factor to convert the distances from cm to m.

If we solve the equation for x, we get:

x = 6.9cm