Moving Charges and Magnetism - Key Vocabulary

Key vocabulary terms and definitions from the lecture on moving charges and magnetism, covering fundamental concepts, laws, and devices.

Oersted's discovery

The finding that a current in a straight wire produces a magnetic field that deflects a nearby compass needle, indicating a link between electricity and magnetism; direction of the field is tangential to circles around the wire and reverses with current.

Magnetic field (B)

A vector field produced by moving charges/currents; exists at every point in space, can vary with time, obeys superposition, and exerts magnetic influence on moving charges and currents.

Lorentz force

The total force on a charge in electric and magnetic fields: F = q(E + v × B); the magnetic component F_mag = q(v × B) depends on charge, velocity, and magnetic field and is perpendicular to both v and B.

Tesla (T)

SI unit of magnetic field strength; defined so that a unit charge moving perpendicular to B at 1 m/s experiences a force of 1 newton.

Gauss (G)

Non-SI unit of magnetic field equal to 10^-4 tesla.

Biot–Savart law

Gives the differential magnetic field dB due to an element dl carrying current I: dB = (μ0/4π) I (dl × r̂)/r^2; describes how currents produce magnetic fields.

Ampere’s circuital law

Relates magnetic field to current: ∮ B · dl = μ0 Ienclosed; for symmetric cases, can reduce to BL = μ0 Ienclosed.

Right-hand rule (for wires)

Grasp the wire with the right hand; thumb along current direction; curled fingers show the direction of the magnetic field circling the wire.

Radius of circular motion in a magnetic field

For a charge moving perpendicular to B, r = mv/(qB); the motion is circular with velocity v and frequency related to B.

Cyclotron frequency

Frequency of circular motion of a charged particle in a uniform magnetic field: ν = qB/(2πm); independent of the particle’s speed or radius.

Helical motion in a magnetic field

If there is a velocity component along B, it remains unchanged while the perpendicular component causes circular motion, resulting in a helical path.

Magnetic moment of a current loop

m = I A; direction given by the right-hand rule; characterizes the loop’s tendency to align with an external B field.

Torque on a current loop

τ = m × B; magnitude τ = IAB sinθ; a loop in a magnetic field experiences a turning torque that tends to align m with B.

Field on the axis of a circular loop

Magnetic field along the axis of a loop of radius R carrying current I at a distance x from the center: B = μ0 I R^2 / [2(R^2 + x^2)^(3/2)]. At the center (x=0): B = μ0 I /(2R).

Magnetic field of a long straight wire

B = μ0 I /(2πr); field lines are concentric circles around the wire and tangential to any circle centered on the wire.

Force between parallel currents

Two long parallel wires with currents I1 and I2 attract if currents are in the same direction and repel if opposite; force per length f = μ0 I1 I2 /(2π d).

Magnetic field inside a solenoid

For a long solenoid, B = μ0 n I, where n is turns per unit length; field is uniform along the axis inside and nearly zero outside.

Magnetic field lines

Imaginary lines indicating direction of magnetic force; they form closed loops and do not begin or end at charges.

Moving coil galvanometer (MCG) torque

A coil in a radial magnetic field experiences torque τ = NIAB; deflection angle φ satisfies φ = NAB I / k, where k is the torsional constant of the spring.

Galvanometer conversion to ammeter

To measure current, a galvanometer is placed in parallel with a small shunt resistor rs; most current bypasses the galvanometer, yielding an effective low resistance close to rs.

Galvanometer conversion to voltmeter

To measure voltage, a galvanometer is placed in series with a large resistor R, increasing total resistance so the galvanometer carries only a small fraction of the circuit current.

Magnetic dipole moment energy and orientation

A current loop behaves as a magnetic dipole with moment m; torque aligns m with external B; potential energy is -m·B (stable when aligned, unstable when anti-aligned).

Relation between μ0, ε0, and c

In vacuum, c^2 = 1/(μ0 ε0); equivalently μ0 ε0 c^2 = 1; this links electromagnetic constants with the speed of light.