Video: How to draw magnetic fields and currents

Vocabulary flashcards covering key concepts from the lecture notes on magnetic fields and currents.

Magnetic field

A vector field describing the magnetic influence of currents and magnets; direction shown by field lines.

Field lines

Curves showing the direction and relative strength of a magnetic field; denser lines indicate stronger fields.

Right-hand rule

A mnemonic to find direction of magnetic field around a current (or force on a moving charge): point the thumb along the current; the curled fingers show field direction; for F = q v × B, positive charges experience the resulting force.

Magnetic field around a straight wire

Around a long straight current-carrying wire, the field forms concentric circles; direction given by the right-hand rule.

B = μ0 I /(2π r)

Magnetic field magnitude at distance r from a long straight wire (valid for very long wires); μ0 is the permeability of free space.

μ0 (magnetic permeability of free space)

Constant relating magnetic field and current in vacuum; μ0 ≈ 4π×10^-7 N/A^2.

ε0 (electric permittivity of vacuum)

Constant describing how electric fields propagate in vacuum; ε0 ≈ 8.85×10^-12 F/m.

Tesla (T)

Unit of magnetic flux density; a strong magnetic field is measured in tesla.

Examples of extreme field strengths

Earth’s strongest pulse ~1,200 T; neutron stars can reach ~10^4–10^11 T.

Current loop

A circular loop of current; behaves like a magnetic dipole with a north and south pole.

Center-of-loop magnetic field direction

The magnetic field at the loop’s center is perpendicular to the loop plane; direction follows the right-hand rule.

North pole of a current loop

The face of the loop that acts as the magnetic north; polarity depends on current direction.

Superposition of magnetic fields

The net field from multiple loops is the vector sum of individual fields.

Solenoid

A coil of many turns that creates an axial magnetic field inside; near-uniform for long solenoids.

Turns per length (n)

n = N/L; number of turns per unit length in a solenoid.

B at solenoid center

For a long solenoid, B ≈ μ0 n I = μ0 (N/L) I.

Solenoid aspect ratio

A longer solenoid (length much greater than diameter) produces a more uniform center field.

Lorentz force

Magnetic force on a moving charge: F = q v × B.

F = q v × B

Equation for the magnetic force on a charge; q is charge, v is velocity, B is magnetic field.

Angle dependence of magnetic force

Force magnitude ∝ sin α, where α is the angle between velocity and magnetic field.

Maximum magnetic force

Occurs when α = 90°, i.e., the velocity is perpendicular to the magnetic field.

Direction of force relative to v and B plane

The magnetic force is always perpendicular to the plane formed by v and B.

Radius of circular motion in a B field

For motion perpendicular to B, r = m v / (|q| B).

Cyclotron motion

Uniform circular motion of a charged particle in a perpendicular magnetic field; used in mass spectrometry.

Helical motion along B lines

If there is a velocity component along B, the particle follows a helical path around the field lines.

Aurora

Visible atmospheric light from charged particles spiraling along Earth’s magnetic field lines and colliding with air.

Electron vs proton deflection

Opposite signs of charge cause opposite directions of the magnetic force for the same v and B.