Question

A long wire carrying a 4.6A current perpendicular to the xy-plane intersects the x-axis at x=-1.6cm. A second, parallel wire carrying a 2.8A current intersects at x=+1.6cm.

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?

Answer 1

Part - A when current flow in same direction say - vl z Let as a distance x from l_1, B_net = 0 B_1 = B_2 implies l_0 . l_1/2 pi x = l_0 . l_2/2 x (3 . 2 - x) implies 4.8 (3 . 2 - x) = 2.8 x implies x = 2.02 cm Part - B When current in opposite direction say l_i rightarrow along - ve z axis, i_2 rightarrow + ve z axis at point P. B_net = 0 B_1 = B_2 l_0 . l_1/2 lambda (3.2 + x_1) = l_0 . i_2/2 pi x_1 implies 4.6 x_1 = 2.8 (3.2 + x) implies x_1 = 9.98 cm from (l_2)