PHYS 2112 Ch 11 – Magnetic Forces and Fields

Magnetic field lines — key property

Always closed loops (no start or end) because there are no magnetic monopoles

Magnetic monopole

An isolated N or S pole — none have ever been found

Magnetic field line direction outside a magnet

Out of the north pole, into the south pole

Field strength from field lines

Strong where lines are close together, weak where far apart; B is tangent to the line

Earth's magnetic field

Earth acts like a bar magnet whose SOUTH pole is near geographic NORTH

Magnetic force on a moving charge

F = qv × B; magnitude F = |q|vB sin θ

Magnetic force on a charge at rest

Zero — only moving charges feel magnetic force

Charge moving parallel to B

Zero magnetic force (sin 0° = 0)

SI unit of magnetic field

Tesla (T) = 1 N/(A·m)

Right-hand rule for F = qv × B

Fingers along v, curl toward B, thumb gives F for a positive charge (reverse for negative)

Symbols ⊙ and ⊗

⊙ = out of the page (arrow tip); ⊗ = into the page (arrow tail)

Work done by magnetic force on a point charge

Zero — force is always perpendicular to velocity, so speed and KE don't change, only direction

Radius of circular motion in a magnetic field

r = mv / (|q|B)

Angular (cyclotron) frequency

ω = |q|B / m (independent of speed)

Period of charged particle in B field

T = 2πm / (|q|B)

Why aurora appear near the poles

Charged particles move nearly parallel to Earth's field there, so the magnetic force (shielding) is ~zero

Applications of circular motion in B fields

Mass spectrometer, cyclotron (e.g. proton therapy)

Force on a current-carrying wire

F = I L × B; magnitude F = ILB sin θ (L points along the current)

Torque on a current loop (N turns)

τ = NIAB sin θ

Magnetic dipole moment of a loop

μ = NIA (direction by right-hand rule); τ = μ × B

Device that runs on torque on a current loop

Electric motor

What creates magnetic fields?

Moving charges (currents). Charges at rest create no magnetic field

Field of a long straight wire

B = μ₀I / (2πr)

Permeability of free space μ₀

4π × 10⁻⁷ T·m/A

Direction of B around a straight wire

Right-hand rule: thumb along current, fingers curl in direction of B (circles around wire)

Field at center of a circular loop (N turns)

B = μ₀NI / (2R)

Right-hand rule for a current loop

Curl fingers with the current; thumb points along B inside the loop

Field inside an ideal solenoid

B = μ₀nI, where n = N/L (turns per length); independent of radius; nearly uniform

Force between two parallel wires

F/l = μ₀I₁I₂ / (2πr)

Parallel wires: same vs opposite current direction

Same direction → attract; opposite directions → repel

Definition of the ampere (parallel wires)

Current in two wires 1 m apart that produces 2 × 10⁻⁷ N per meter of force on each