PHYS 1120 — EXAM 2 REVIEW

Ohm's Law

The current through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. V = IR. Only applies to ohmic materials (constant R). A resistor's R does not depend on V or I.

Kirchhoff's Junction Rule (KCL)

At any junction in a circuit, the total current entering equals the total current leaving. ΣI_in = ΣI_out. Based on conservation of charge — charge cannot accumulate at or vanish from a junction.

Kirchhoff's Loop Rule (KVL)

Around any closed loop in a circuit, the sum of all voltage gains and drops is zero. ΣV = 0. Based on conservation of energy — a charge returning to its starting point must have the same potential energy.

Joule's Law (Resistive Heating)

Current through a resistor converts electrical energy irreversibly into thermal energy (heat). P = I²R = V²/R = IV. The energy is lost and cannot be stored — unlike a capacitor which stores energy in its electric field.

Series vs. Parallel Principle

Series: Same current through all elements, voltages add. Adding R increases total resistance. Parallel: Same voltage across all elements, currents add. Adding R decreases total resistance (more paths for current).

Lorentz Force Law

A charged particle moving through a magnetic field experiences a force perpendicular to both its velocity and the field. F = qv × B. The force is maximum when v ⊥ B and zero when v ∥ B. Because F ⊥ v always, the magnetic force does no work and cannot change a particle's speed — only its direction.

Right-Hand Rule (Principle)

For force: Point fingers along v, curl toward B, thumb points in F direction (for + charge). For negative charges, flip F. For wire's B field: Thumb along current I, fingers curl in B direction. For solenoid: Curl fingers with current, thumb = N pole.

Biot-Savart Law

Every small segment of current-carrying wire contributes to the magnetic field. For a long straight wire: B = μ₀I/(2πr). B decreases as 1/r from the wire. Field lines form concentric circles around the wire.

Ampère's Law

The line integral of B around any closed loop equals μ₀ times the total current enclosed. Used to derive B inside a solenoid: B = μ₀nI (uniform inside, ≈0 outside). Also gives the field of straight wires and toroids.

Superposition Principle

The net magnetic field at any point is the vector sum of fields from all sources. This is how we find where B = 0 between parallel wires, or add B fields from a wire and a loop. Always add as vectors (direction matters!).

Gauss's Law for Magnetism

There are no magnetic monopoles. Every magnetic field line that enters a closed surface must also exit it. The net magnetic flux through any closed surface is zero: ∮B·dA = 0. This is why magnets always have both N and S poles.

Force Between Parallel Currents

Same direction currents attract. Opposite direction currents repel. Why? Each wire sits in the other's B field, and F = IlB gives a force toward or away. F/l = μ₀I₁I₂/(2πd). This defines the SI ampere.

Faraday's Law of Electromagnetic Induction

A changing magnetic flux through a circuit induces an EMF (voltage). ε = −N(dΦ/dt). The EMF depends on the rate of change of flux, not the flux itself. Flux can change by changing B, A, or the angle φ between B and the area normal. A constant flux produces zero EMF regardless of how large B is.

Lenz's Law

The induced current flows in a direction that opposes the change in flux that caused it. If flux is increasing, induced current creates opposing B. If flux is decreasing, induced current supports the existing B. This is a consequence of conservation of energy — if it didn't oppose, you'd get perpetual motion. The minus sign in Faraday's law encodes Lenz's law.

Motional EMF

A conductor moving through a magnetic field develops a voltage across it. ε = vBL (when v, B, L mutually ⊥). The magnetic force pushes charges to one end, creating a potential difference. If v is parallel to B or parallel to L, no EMF is induced.

Magnetic Flux

Φ = BA cosφ where φ is the angle between B and the area normal (NOT the surface). Φ is maximum when B ⊥ surface (φ = 0°), and zero when B ∥ surface (φ = 90°). Units: Weber (Wb) = T·m².

Transformer Principle

AC in a primary coil creates a changing B that induces EMF in a secondary coil. V₂/V₁ = N₂/N₁. Power is conserved: V₁I₁ = V₂I₂. Step-up (N₂ > N₁) increases voltage but decreases current. Does NOT work with DC — requires changing flux.

Self-Induction & Back-EMF

A changing current in a coil induces an EMF in itself that opposes the change (Lenz's law applied to its own flux). ε_L = −L(dI/dt). An inductor resists changes in current. When a switch is opened, the rapid dI/dt can produce a large voltage spike. Energy stored: E = ½LI².

Conservation of Energy

Energy cannot be created or destroyed, only transformed. In circuits: battery chemical energy → electrical → heat (resistors) or stored (capacitors/inductors). This principle underlies Kirchhoff's loop rule, Lenz's law, and why magnetic force does no work (it only redirects, never creates or destroys KE).

Conservation of Charge

Electric charge can neither be created nor destroyed. The total charge in a closed system is constant. This underlies Kirchhoff's junction rule and why current is the same through all elements in series.

Principle of Superposition

The net electric or magnetic field at any point is the vector sum of all individual fields. This allows us to analyze complex circuits (superposition theorem) and find B from multiple wires by adding each wire's contribution as vectors.

Work-Energy Theorem

The net work done on a particle equals its change in kinetic energy: W_net = ΔKE. Since magnetic force is always ⊥ to velocity, it does zero work → KE is unchanged → speed is constant in a magnetic field. Only direction changes (circular orbit).

Newton's Second Law (applied to charged particles)

F = ma. For circular motion in B: qvB = mv²/R → R = mv/(qB). The magnetic force provides centripetal acceleration. Larger mass or speed → larger radius. Stronger B → tighter circle.