Lorentz Force on a Moving Charge

Identify q, m, v, B, and angle theta. Choose F = qvB sin theta for magnetic force. For circular motion with perpendicular entry, equate qvB to mv^2/r. Substitute SI units. Decide force direction using v x B and reverse it for a negative charge.

Draw v tangent to the circular path, B perpendicular to the plane, and F toward the centre. Use dot for field out of page and cross for field into page. Label charge sign because force direction reverses for negative charge.

Using r = qB/(mv) reverses the formula and gives a physically wrong result, where faster particles would have smaller radius.

Lorentz force is the total force on a charge q moving with velocity v in the presence of electric field E and magnetic field B, given by F = q(E + v x B).

Lorentz force is the total force on a charge q moving with velocity v in the presence of electric field E and magnetic field B, given by F = q(E + v x B). F = q(E + v x B). Magnetic force magnitude: F_B = qvB sin theta. For perpendicular entry into uniform B: qvB = mv^2/r, so r = mv/(qB) using magnitude of q. q is in coulomb, v in m s^-1, B in tesla, F in newton, m in kg, r in metre. Use this when the magnetic field is uniform and motion is perpendicular to B for circular motion. An electron entering a uniform magnetic field at right angles follows a circular path. The magnetic force changes the direction of velocity but not the speed because it is always perpendicular to the motion.

The electric part qE acts whether the charge is moving or at rest. The magnetic part q(v x B) acts only when the charge has velocity with a component perpendicular to the magnetic field. Its direction is perpendicular to both v and B, and it is reversed for a negative charge. If v is perpendicular to B and there is no electric field, the magnetic force provides centripetal force, so the charge moves in a circular path. F = q(E + v x B). Magnetic force magnitude: F_B = qvB sin theta. For perpendicular entry into uniform B: qvB = mv^2/r, so r = mv/(qB) using magnitude of q. q is in coulomb, v in m s^-1, B in tesla, F in newton, m in kg, r in metre. Use this when the magnetic field is uniform and motion is perpendicular to B for circular motion. A proton of mass 1.67 x 10^-27 kg and charge 1.6 x 10^-19 C enters a 0.20 T magnetic field with speed 2.0 x 10^6 m s^-1 perpendicular to the field. r = mv/(qB) = (1.67 x 10^-27 x 2.0 x 10^6)/(1.6 x 10^-19 x 0.20) = 0.104 m approximately. The proton follows a circle of radius about 10.4 cm. Usually asked as a numerical on radius or force, a direction question using right-hand rule, or an assertion-reason item on why magnetic force does no work. Using r = qB/(mv) reverses the formula and gives a physically wrong result, where faster particles would have smaller radius.