The force on a moving charge.

A rotatable 3D view of v, B and F = q v × B for a positive or negative charge, with |F| = qvB sin θ.

For an electron moving along +x, choose the B direction that pushes it along +z (B along −y), then find the angle at which the force is half its maximum (30°)

Using the positive-charge rule for an electron.

• In 1820 Oersted saw a compass needle swing when a current flowed in a nearby wire. The needle sets itself along the tangent to a circle centred on the wire; reversing the current reverses it, and a bigger current or a closer needle deflects it more.
• Iron filings round a current-carrying wire settle into concentric circles. Oersted's conclusion: moving charges, that is currents, set up a magnetic field in the space around them.
• Drawing convention: a dot (⊙) is a current or field coming out of the page, a cross (⊗) one going into it, like the tip and the tail feathers of an arrow.
• The magnetic field B is a vector field, defined at every point, and it obeys superposition: the fields of several sources add as vectors, just as electric fields do.
• A charge q moving with velocity v through fields E and B feels the Lorentz force F = q[E + v × B]. The electric part does not care about motion; the magnetic part does.
• The magnetic force q(v × B) is zero for a charge at rest and zero when v is parallel or antiparallel to B. It is perpendicular to both v and B, with direction from the right-hand (screw) rule, and it reverses for a negative charge.
• Its size is qvB sin θ, where θ is the angle between v and B. This defines the unit: 1 tesla (T) is the field that pushes 1 N on 1 C moving at 1 m/s at right angles to it, so 1 T = 1 N s C⁻¹ m⁻¹.
• The tesla is large. The non-SI gauss is 10⁻⁴ T, and the earth's field is about 3.6 × 10⁻⁵ T.

Teaching this idea? Put the simulation on your own page or LMS with this code.