Describe magnetic fields and the field produced by an electric current, apply $F_B = qvB$ to the force on a moving charge in a magnetic field, and explain the force on a current-carrying wire that underlies the electric motor.

What this topic is asking

This dot point introduces magnetism and its deep link to electric current. The Physical Setting/Physics course asks you to describe magnetic fields and their field lines, to recognize that an electric current produces a magnetic field, to calculate the force on a moving charge in a magnetic field with $F_B = qvB$, and to understand the force on a current-carrying wire that makes electric motors turn (the motor effect). The Regents tests field directions, the conditions for a magnetic force, and the $F_B = qvB$ calculation.

Magnetic fields and field lines

Like magnetic poles repel and unlike poles attract, echoing electric charges, but magnetic poles always come in north-south pairs; a single isolated pole has never been found. Field lines are closer together where the field is stronger (near the poles) and never cross. Reading field-line diagrams and the direction of the field is a common Regents task.

The magnetic field of a current

This connection, that electricity and magnetism are two aspects of one phenomenon, is the heart of the strand. A current creates a magnetic field (electromagnetism), and, conversely, a changing magnetic field creates a current (electromagnetic induction). Electromagnets are used in motors, relays, loudspeakers and maglev systems.

The force on a moving charge

The dependence on the angle is important: only the component of velocity perpendicular to the field contributes, so a charge moving along the field lines feels no force. Because the force is always perpendicular to the velocity, it changes the charge's direction but not its speed, which makes charged particles move in circles in a uniform field (as in a mass spectrometer). The Regents most often gives the perpendicular case so $F_B = qvB$ applies directly.

The motor effect

The moving charges in a current-carrying wire in a magnetic field each feel the $F_B = qvB$ force, and together they produce a force on the wire. The size of this force is $F = BIL$ (recall, not on the tables), where $I$ is the current and $L$ the length of wire in the field, and its direction is perpendicular to both the current and the field. This motor effect is what makes an electric motor turn: a current-carrying coil in a magnetic field experiences forces that rotate it. Reversing the current or the field reverses the force.

Reference Tables note

The equation $F_B = qvB$ is printed in the Electricity section of the Reference Tables (it is the only magnetic equation there). The force on a current-carrying wire, $F = BIL$, is not printed, so you recall it. The field-line conventions, the right-hand rules for direction, and the fact that a current produces a magnetic field are qualitative ideas the Regents expects you to know rather than read from the booklet.

Try this

Q1. State the condition under which a moving charge feels the maximum magnetic force, and the condition for zero force. [2 points]

• Cue. Maximum when the velocity is perpendicular to the field; zero when the velocity is parallel to the field.

Q2. A $3.0$ C charge moves at $2.0$ m/s perpendicular to a $0.40$ T field. Calculate the magnetic force. [2 points]

• Cue. $F_B = qvB = (3.0)(2.0)(0.40) = 2.4$ N.