Physics · Moving Charges And Magnetism · NEET
Wire 1 makes a magnetic field B1 = mu0 I1 / (2 pi d) at wire 2. Using the right-hand rule, this field points into the page at wire 2's location (for the usual figure). Wire 2 carries current I2 in that field, so it feels a force F = I2 L x B1. Applying the direction rule, the force on wire 2 points back toward wire 1. By symmetry wire 1 is pulled toward wire 2. So same-direction currents ATTRACT. This is the opposite of charges: like (parallel) currents attract, unlike (antiparallel) currents repel.
The wires are treated as infinitely long, so the total force would be infinite. Instead we quote force per metre of wire, written F/L. The formula is F/L = mu0 I1 I2 / (2 pi d) in newtons per metre. To get the actual force on a piece of wire of length L, multiply by L: F = (mu0 I1 I2 / 2 pi d) x L.
It comes in two steps. Wire 1's field at distance d is B = mu0 I1 / (2 pi d) - this 2 pi is from the field of a long straight wire (Ampere's law). Wire 2 then feels F/L = B x I2 = mu0 I1 I2 / (2 pi d). So the single 2 pi in the final answer is just the 2 pi from the straight-wire field. Do not add an extra 2 - a common slip is writing 4 pi.
Set I1 = I2 = 1 A and d = 1 m in F/L = mu0 I1 I2 / (2 pi d). With mu0 = 4 pi x 10^-7, F/L = (4 pi x 10^-7)(1)(1) / (2 pi x 1) = 2 x 10^-7 N/m. So one ampere is the steady current which, kept in two very long straight parallel wires 1 metre apart in vacuum, makes each wire feel a force of 2 x 10^-7 newton per metre of length.
An arrangement of three parallel straight wires placed perpendicular to the plane of paper carrying the same current 'I' along the same direction is shown (wires A and C each at distance d from middle wire B, with lines BA and BC at 90 degrees). The magnitude of the force per unit length on the middle wire 'B' is:
Two infinitely long parallel conducting wires A and B carry currents I and 2I in the same direction. Wire A has mass per unit length lambda and lies on an insulated floor. Wire B is fixed at height h above the floor. The minimum h so that wire A does not rise from the floor is (g = acceleration due to gravity, mu0 = permeability of free space):
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Force per unit length F/L = mu0 I1 I2 / (2 pi d), where I1 and I2 are the currents, d is the gap, and mu0 = 4 pi x 10^-7 T m/A. Multiply by length L for the total force.
Currents in the same direction (parallel) attract each other. Currents in opposite directions (antiparallel) repel. This is the reverse of electric charges.
One ampere is the steady current which, kept in two very long straight parallel wires placed 1 metre apart in vacuum, produces a force of 2 x 10^-7 newton on each metre of length.
Yes. Even if the currents I1 and I2 differ, both wires feel the same force per unit length, because the formula I1 x I2 is symmetric. This agrees with Newton's third law.
The wires are taken as infinitely long, so the total force would be infinite. Force per metre (N/m) is finite and is what NEET formulas quote.
