A moving charge in a magnetic field experiences magnitude F=∣q∣vB sinθ, where θ is between velocity and field. The direction for a positive charge follows v×B; reverse it for a negative charge. A charge moving parallel to B has no magnetic force. At right angles, F=∣q∣vB. The force is perpendicular to velocity, so an ideal magnetic field alone does no work on the particle.
A straight current-carrying length L has force F= BIL sinθ in a uniform external field, using conventional current direction for the cross-product rule. Only the portion inside the field belongs in L. Electric forces can act on stationary charge and change speed; magnetic forces depend on velocity and, acting alone, change direction without changing kinetic energy.
Example 1
A+2.00×10−19C particle moves east at 3.00×105ms−1 through B=0.400T north. Find force.
F=qvB=2.40×10−14N, vertically upward by east × north. A negative charge would be forced downward.
Example 2
A 0.150m wire carries 4.00 A perpendicular to 0.200T. Find force.
F=BIL=0.200×4.00×0.150=0.120N.
Watch out: The magnetic force is perpendicular to motion, so it changes direction but supplies no kinetic-energy gain by itself.