Question

A long wire carrying IA = 4.0 A  of current perpendicular to the xy-plane intersects the x-axis at x=−2.0cm . A second, parallel wire carrying IB = 3.5 A  of current intersects the x-axis at x=+2.0cm . (As illustrated in the figure, the two currents are either into or out of the page.)

At what point on the x-axis is the magnetic field zero if the two currents are in opposite directions?

IA +2 B 2

Answer 1

I_A = 4A I_B = 3.5 A Both the currents are in opposite direction Net I_A is Into plane, I_B is out of plane, two fields B_A and B_B due to two currents, will be additive between + 2 cm and - 2 cm Let field at p is zero (use right hand Thumb Rule) B_A = mu_0 I_A/2 pi (x + 2): B_B = mu_0 I_B/2 pi (x - 2) B_A = B_b Therefore I_A/x + 2 = I_B/x - 2 4x - 8 = 3.5 x + 7 = 0.5 x = 15 cm Therefore x = 30 cm