Grade 12 Physics · Wires in the field
A current is a crowd of moving charges
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A current is a crowd of moving charges

Put a whole current in a field and every moving charge in it gets the same sideways shove — added up, that is the motor effect: F=BILsinθF = BIL\sin\theta, read aloud F equals B I L sine theta. FF is the force on the wire in newtons; BB is the field in teslas; II is the current in amperes; LL is the length of wire actually inside the field, in metres — not the length of the whole wire, and examiners know you know that; and θ\theta is the angle between the wire and the field lines, with the same sine as before.

Two parallel wires need no external magnet at all: each one sits in the field the other makes, so they push on each other. F=μ0I1I22πdF = \dfrac{\mu_0 I_1 I_2 \ell}{2\pi d}. Here I1I_1 and I2I_2 are the two currents in amperes (the subscripts only number the wires, no order implied), \ell is the length of the parallel run in metres, dd is the separation between them in metres, and μ0\mu_0 is the permeability of free space, 4π×107 Tm/A4\pi \times 10^{-7}\ \mathrm{T \cdot m/A}. Learn the tidy consequence and you can do these in your head: μ02π=2×107\dfrac{\mu_0}{2\pi} = 2 \times 10^{-7} exactly.

Direction, in one line: currents running the SAME way attract, opposite ways repel — the opposite of what charges do, and worth saying out loud twice. And read the question before you answer it: force PER METRE and force on the WHOLE run differ by a factor of \ell, and that is the single most reliable mark lost on this page.