Question

A straight segment OC (of length L) of a circuit carrying a current ‘i’is placed along the X-axis as shown in figure.Two infinitely long straight wires A and B, each extending from z =  ∞ to + ∞, are fixed at y = –a and y = + a respectively. as shown in the figure. If the wires A and B each carry a current ‘i’into the plane of the paper, obtain the expression for the force acting on the segment OC. What will be force of OC if the current in the wire B is reversed ?

Answer 1

(a) Let us assume a segment of length dx at a point P, a distance x from the centre shown in figure.

⊙ is the positive Z-direction and

⊗ is the negative Z-direction and

Magnetic field at P due to current in wires A and B will be in the directions perpendicular to AP and BP respectively as shown.

Therefore, net magnetic field at P will be along negative y= axis as shown

Therefore, force on the element will be (F = ilB)

∴ Total force on the wire will be

(in negative z-axis)

Hence

(b) If current in wire B is reversed, then magnetic fields due to A and B will be in the directions shown in figure. i.e., net magnetic field Vector B_net will be along positive x-axis and since current is also along positive x-axis, force on wire OC will be zero.

Note : Vector B is not necessarily parallel to BP.