Use F = qv × B and the Right-Hand Rules, and Reverse the Result for Negative Charge
Magnetism questions ask about the direction of a force on a moving charge, the direction of curvature of a track, or the field produced by a current. The right-hand rule gives all three, and the only extra step is reversing the result for a negative charge.
Electricity questions depend on identifying charge, a conducting path and the condition that controls current or magnetic effect.
Force on a moving charge
For a positive charge, the direction of v × B is the direction of the force; for a negative charge such as an electron it is the opposite. An electron projected east and deflected north needs v × B to point south: with east = +x and north = +y, v × B must be along -y, and x × B = -y when B is +z, so the field points upward. A magnetic force is always perpendicular to the velocity, so it changes the direction of motion but not the speed;
A neutral particle such as a neutron feels no magnetic force.
Reading a curved track
In a cloud chamber the sense of curvature tells the sign of the charge for a given direction of travel. Reversing both the sign of the charge and the direction of travel gives the same curvature, so a track that suits a proton or an α particle going from p to q is also compatible with an electron going from q to p, but not with a neutron. A larger charge-to-mass ratio, or a smaller momentum, gives a tighter curve.
Fields of currents
For a hairpin conductor with currents in opposite directions on two parallel arms, the fields of the two arms add in the region between them and partly cancel outside.
it falls to about half this value at the ends and is negligible outside, so a point at the centre of a long solenoid has the largest field.
OlympIQ exam lens
- ✓F = q v × B; reverse the direction for a negative charge
- ✓The magnetic force never changes speed; the circular radius is m v / (q B)
- ✓Reversing both the charge sign and the direction of travel gives the same curvature; neutral particles go straight
- ✓Long wire: B = μ0 I / 2π r; two opposite currents add between the wires
- ✓Long solenoid: B = μ0 n I, uniform inside, about half at the ends, nearly zero outside
Do not forget the sign of an electron. The right-hand rule gives the force on a positive charge; for an electron the force is opposite, so a field direction worked out for a positive charge is reversed.
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