PHYS 1120 Exam 2 Review

Q1Force Direction on Proton (RHR 2)

CONCEPT
A positive charge moving through a magnetic field experiences a force: F = qvB sinθ

METHOD
Use Right-Hand Rule #2: Point fingers in direction of v, curl toward B. Thumb = F direction (for + charge).

(a) v → (right), B ↑ (up) ⇒ F out of page (⊙)

(b) v ↑ (up), B ⊗ (into page) ⇒ F right (→)

(c) v ⊙ (out of page), B → (right) ⇒ F up (↑)

MNEMONIC: "FBI" — F = Thumb, B = Curl-to, I(v) = Fingers point

For NEGATIVE charges (electrons), flip the force direction!

Q2Find B from Known v and F (RHR 2 Reverse)

CONCEPT
Given v and F directions, find B by reversing RHR 2. Point fingers along v, thumb along F — palm pushes toward B.

Ex 1: v → (right), F ↑ (up) ⇒ B out of page (⊙)

Ex 2: v → (right), F ⊗ (into page) ⇒ B down (↓)

KEY
For electrons: apply RHR as if positive, then flip B direction.

F = qvB ⇒ B = F/(qv)

Common mistake: forgetting to flip for negative charges!

Q3Forces Between Parallel Wires

RULE
Same direction currents → ATTRACT
Opposite direction currents → REPEL

F/ℓ = μ₀I₁I₂ / (2πR₁₂)

WORKED EXAMPLE
I₁ = I₂ = 25 A, R = 35 cm = 0.35 m, ℓ = 15 cm = 0.15 m

F/ℓ = (4π×10⁻⁷)(25)(25) / (2π)(0.35) = 3.57×10⁻⁴ N/m
F = (3.57×10⁻⁴)(0.15) ≈ 5.4×10⁻⁴ N

MNEMONIC: "Same = Snuggle, Opposite = Oh no!" (attract vs repel)

Q4+ Charge in B Out of Page → Clockwise Circle

CONCEPT
A positive charge moving in a uniform B field follows a circular path. F is always perpendicular to v, acting as centripetal force.

R = mv / (qB)

DIRECTION
+ charge enters B⊙ (out of page) moving right → RHR gives F downward → curves down → Clockwise circle

ANSWER
Clockwise circular path

Negative charge in same setup → COUNTERCLOCKWISE

Q5Variable Resistor → Induced Current in Loop A

SETUP
Circuit with variable resistor (slider). Nearby loop A detects induced current.

CHAIN OF REASONING
Slider moves LEFT → R decreases → I increases (V=IR, V fixed)
→ B increases (B ∝ I) → Φ through loop A increases
→ Lenz's Law: induced current opposes increase
→ Induced B opposes original B

ANSWER
(b) Counterclockwise in loop A

MNEMONIC: Lenz = "Nature is Lazy" — opposes all change

Q6KE of Particle in Circular Path

KEY PRINCIPLE
Magnetic force is always perpendicular to velocity. Therefore:

W = F · d · cos(90°) = 0

Zero work done → No change in kinetic energy → Speed stays constant (only direction changes)

ANSWER
(c) Remains constant — F ⊥ v means W = 0 means ΔKE = 0

B field changes DIRECTION of velocity, never SPEED!

Q7Steady 1.5A in Solenoid → Loop Current

KEY PRINCIPLE
Faraday's Law: EMF is induced only when flux is changing.

ε = −dΦ/dt

Steady (constant) current → Constant B → Constant Φ → dΦ/dt = 0 → ε = 0 → No induced current

ANSWER
ZERO — a steady current produces no change in flux

This is the #1 Faraday trap! "Steady" = "constant" = NO induction. Only CHANGING currents induce.

Q8Bar Magnet Through Loop

PHASE 1: APPROACHING (N-end down)
Φ increasing → Lenz opposes increase → induced B opposes magnet's B → CCW current (from above) → Loop REPELS magnet

PHASE 2: LEAVING (N-end still down)
Φ decreasing → Lenz opposes decrease → induced B supports magnet's B → CW current (from above) → Loop ATTRACTS magnet

ANSWER
Current REVERSES direction as magnet passes through. Approaching: CCW. Leaving: CW.

MNEMONIC: "Coming in? Push away. Going out? Pull back." — Lenz always fights change.

Q94× Speed → 4R Radius

FORMULA

R = mv / (qB)

R is directly proportional to v (m, q, B held constant).
If v → 4v, then R → 4R

ANSWER
New radius = 4R (radius scales linearly with speed)

Don't confuse with KE (KE ∝ v²) — radius is LINEAR in v!

Q10Solenoid + Bar Magnet → Attract (Unlike Poles)

METHOD
1. Use RHR 1 to find solenoid polarity: curl fingers in direction of current, thumb points to N pole.
2. Compare solenoid pole facing magnet to magnet pole facing solenoid.
3. Unlike poles → ATTRACT. Like poles → REPEL.

ANSWER
Unlike poles face each other → ATTRACT (pull toward each other)

MNEMONIC: RHR 1 — "Curl with Current, Thumb = North"

Q11Electron Beam Between Magnets

SETUP
Electron beam travels horizontally between magnets. B field points downward.

METHOD
1. Pretend it's a POSITIVE charge → apply RHR 2
2. v horizontal, B down → RHR gives force in one direction
3. FLIP for electron (negative charge) → force in opposite direction → UPWARD

ANSWER
(c) Accelerated upward — "accelerated" here means direction changes, not speed

"Accelerated" in physics = any change in velocity (including direction). B field can accelerate without changing speed!

Q12Switch Opens → Voltmeter Reading Increases

CONCEPT
When switch S opens, a parallel branch is removed from the circuit.

CHAIN
Remove parallel branch → Total R increases → Current from battery may decrease → But the voltage redistribution across remaining components changes → Voltmeter reading INCREASES

ANSWER
Voltmeter reading INCREASES when switch opens

WHY
Opening the switch removes a current path. The remaining resistor now gets a larger share of the battery voltage (less voltage dropped elsewhere).

Q13R and 4R in SERIES, P(4R)=40W → P(R)=?

KEY PRINCIPLE
In SERIES, current I is the same through all resistors.

P = I²R ⇒ P ∝ R (same I)

LOGIC
P(4R) = I²(4R) = 40W
P(R) = I²(R) = 40W ÷ 4 = 10W

ANSWER
P(R) = 10W — In series, power is proportional to resistance

Series: P ∝ R (bigger R = MORE power)
Don't confuse with parallel!

Q14R and 5R in PARALLEL, P(R)=50W → P(5R)=?

KEY PRINCIPLE
In PARALLEL, voltage V is the same across all resistors.

P = V²/R ⇒ P ∝ 1/R (same V)

LOGIC
P(R) = V²/R = 50W
P(5R) = V²/(5R) = 50W ÷ 5 = 10W

ANSWER
P(5R) = 10W — In parallel, power is INVERSELY proportional to resistance

Parallel: P ∝ 1/R (bigger R = LESS power)
OPPOSITE of series!

Q15Alpha Particle in B Field (INTERACTIVE)

GIVEN
Alpha particle: q = 2e = 3.2×10⁻¹⁹ C, m = 6.64×10⁻²⁷ kg

R = mv/(qB), Diameter = 2R, a = qvB/m

Speed v: 35.6 km/s

Magnetic Field B: 1.10 T

R = 0.670 mm | Diameter = 1.340 mm
a = 1.89×10⁹ m/s²

Alpha has charge 2e (not 1e)! Forgetting = double the radius.

Q16Rod on Rails (INTERACTIVE)

GIVEN
Rod of length L = 0.50 m slides on rails, external resistor R = 1.50 Ω

ε = BLv, I = ε/R, F = BIL

Rod Speed v: 7.50 m/s

Magnetic Field B: 0.80 T

ε = 3.000 V | I = 2.000 A | F = 0.800 N

VIFf CHAIN
v (speed) → ε (EMF) → I (current) → F (force on rod)
Each depends on the previous!

Force on the rod OPPOSES motion (Lenz's Law applied mechanically)

REFSeries vs Parallel Power Comparison

Property	SERIES	PARALLEL
What's shared?	Current I (same through all)	Voltage V (same across all)
Power formula	P = I²R	P = V²/R
Power vs R	P ∝ R (more R = more P)	P ∝ 1/R (more R = less P)
Bigger resistor gets...	MORE power	LESS power
Example	R & 4R: P(4R) = 4×P(R)	R & 5R: P(R) = 5×P(5R)
Common mistake	Using V²/R (wrong! V differs)	Using I²R (wrong! I differs)

Formula	Variables	Used In
F = qvB sinθ	Force on moving charge	Q1, Q2, Q11
R = mv/(qB)	Circular orbit radius	Q4, Q9, Q15
F/ℓ = μ₀I₁I₂/(2πd)	Force between parallel wires	Q3
ε = −dΦ/dt	Faraday's Law (EMF)	Q5, Q7, Q8
ε = BLv	Motional EMF	Q16
B = μ₀nI	Solenoid B field	Q10

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SCIENTIFIC CALCULATOR

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LAWS, PRINCIPLES & THEORIES

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CH 19 — Circuit Laws

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).

CH 20 — Magnetism Laws

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.

CH 21 — Induction Laws

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.

Foundational Principles

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.

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FORMULA SHEET — ALL EXAM TOPICS

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CH 19 — DC Circuits

V = IROhm's law

R = ρL/AResistance from resistivity

P = IV = I²R = V²/RPower dissipated

R_s = R₁+R₂+...Series: same I, V adds

1/R_p = 1/R₁+1/R₂+...Parallel: same V, I adds

ε = I(R+r)EMF with internal resistance

V_term = ε − IrTerminal voltage

ΣV = 0Kirchhoff's loop rule

ΣI_in = ΣI_outKirchhoff's junction rule

q(t) = Cε(1−e^(-t/RC))RC charging

τ = RCRC time constant

CH 20 — Magnetic Forces

F = |q|vB sinφForce on moving charge

F = IlB sinφForce on current-carrying wire

R = mv/(|q|B)Circular orbit radius

T = 2πm/(|q|B)Cyclotron period

v = E/BVelocity selector

τ = NIAB sinφTorque on current loop

μ = NIAMagnetic moment

B = μ₀I/(2πr)Long straight wire

B = μ₀NI/(2R)Center of circular loop

B = μ₀nIInside solenoid (n=N/L)

F/l = μ₀I₁I₂/(2πd)Force between parallel wires

CH 21 — Electromagnetic Induction

Φ = BA cosφMagnetic flux

ε = −N(dΦ/dt)Faraday's law

ε = vBLMotional EMF

ε = BLv sinθMotional EMF (angle)

Lenz's LawInduced I opposes ΔΦ

ε₂/ε₁ = N₂/N₁Transformer voltage ratio

V₁I₁ = V₂I₂Transformer power conservation

E_L = ½LI²Energy stored in inductor

i(t) = (ε/R)(1−e^(-Rt/L))RL circuit growth

τ_L = L/RRL time constant

Key Rules & Mnemonics

RHR (Force)Fingers=v, curl=B, thumb=F (+ charge)

RHR (Wire B)Thumb=I, fingers curl=B direction

Lenz's LawInduced current opposes the CHANGE in flux

W_mag = 0Magnetic force does NO work (F ⊥ v)

SeriesSame I → P=I²R → bigger R = more P

ParallelSame V → P=V²/R → bigger R = less P

φ in fluxAngle between B and area NORMAL, not surface

Same-dir IWires attract; opposite-dir wires repel

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UNITS, CONVERSIONS & CONSTANTS

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FUNDAMENTAL CONSTANTS

Symbol	Name	Value
e	Elementary charge	1.602 × 10⁻¹⁹ C
m_e	Electron mass	9.109 × 10⁻³¹ kg
m_p	Proton mass	1.673 × 10⁻²⁷ kg
m_α	Alpha particle mass	6.644 × 10⁻²⁷ kg
μ₀	Permeability of free space	4π × 10⁻⁷ T·m/A
ε₀	Permittivity of free space	8.854 × 10⁻¹² F/m
k	Coulomb constant	8.988 × 10⁹ N·m²/C²
c	Speed of light	3.00 × 10⁸ m/s
g	Gravitational acceleration	9.80 m/s²

UNITS & DIMENSIONS

Quantity	Unit	Symbol	Equivalent
Current	Ampere	A	C/s
Charge	Coulomb	C	A·s
Voltage / EMF	Volt	V	J/C = W/A
Resistance	Ohm	Ω	V/A
Resistivity	Ohm-meter	Ω·m	—
Power	Watt	W	V·A = J/s
Energy	Joule	J	V·C = W·s
Magnetic field	Tesla	T	kg/(A·s²) = V·s/m²
Magnetic field	Gauss	G	10⁻⁴ T
Magnetic flux	Weber	Wb	T·m² = V·s
Capacitance	Farad	F	C/V
Inductance	Henry	H	V·s/A = Ω·s
Frequency	Hertz	Hz	1/s
Force	Newton	N	kg·m/s²
Torque	Newton-meter	N·m	—

SI PREFIX CONVERSIONS

Prefix	Symbol	Factor	Example
Tera	T	10¹²	1 THz = 10¹² Hz
Giga	G	10⁹	1 GW = 10⁹ W
Mega	M	10⁶	1 MΩ = 10⁶ Ω
kilo	k	10³	1 kV = 1000 V
centi	c	10⁻²	1 cm = 0.01 m
milli	m	10⁻³	1 mA = 0.001 A
micro	μ	10⁻⁶	1 μF = 10⁻⁶ F
nano	n	10⁻⁹	1 nC = 10⁻⁹ C
pico	p	10⁻¹²	1 pF = 10⁻¹² F

COMMON RESISTIVITY VALUES

Material	ρ (Ω·m)	Type
Silver	1.47 × 10⁻⁸	Conductor
Copper	1.72 × 10⁻⁸	Conductor
Aluminum	2.63 × 10⁻⁸	Conductor
Tungsten	5.25 × 10⁻⁸	Conductor
Iron	9.68 × 10⁻⁸	Conductor
Nichrome	1.00 × 10⁻⁶	Alloy

🎙️ Red border = from live lecture (Omi) | No border = from textbook/manual entry

🎙️ LECTURE NOTES — Magnetism & Charged Particles (April 1)

L1Magnetic Fields: Bar Magnets vs Solenoids

KEY CLAIM FROM LECTURE
"There's nothing a natural magnet does that we cannot produce with a current." — Any bar magnet field pattern can be replicated by the right geometry of current-carrying coils.

FIELD LINES
Magnetic field lines go out of North, into South (outside the magnet). Inside the magnet, they go South→North. A solenoid produces the same pattern — uniform B inside, with identifiable N and S poles.

SOLENOID → BAR MAGNET
Use right-hand grip rule: wrap fingers in direction of current → thumb points to North pole. Then replace the solenoid with a bar magnet that has matching N/S orientation.

🧠 From lecture: "Put a black box on top — you can't tell if it's a bar magnet or a solenoid producing the field."

L2The Two Right-Hand Rules (from lecture)

RHR #1 — GRIP RULE (for currents → B field)
Thumb = direction of current (I)
Curled fingers = direction of magnetic field lines (B)
Used for: straight wires, solenoids, any current-producing geometry

RHR #2 — FLAT HAND (for force on charges)
Thumb = velocity (v) of positive charge
Fingers = magnetic field (B)
Palm/force = out of palm (F)
For negative charge: force is in the opposite direction

⚠️ Lecture trap: If v and B end up parallel in your setup, something is wrong! F = qvB sin(θ), and sin(0°) = 0 → no force. You cannot get circular motion with parallel v and B.

WIRE FORM
For a current-carrying wire: F = ILB sinθ
Thumb = I (current direction), curl toward B → palm = F direction

L3Charged Particle Circular Motion in B Field

SETUP
When v ⟂ B: magnetic force is always perpendicular to velocity → circular motion at constant speed

DERIVATION (done on board)
Magnetic force = centripetal force:
|q|vB = mv²/r
Solve for radius:
r = mv / (|q|B)

KEY RELATIONSHIPS

• Velocity doubles (2v) → radius doubles (2r)

• Charge doubles (2q) → radius halves (r/2) — "larger charge = smaller radius"

• Mass quadruples (4m) → radius quadruples (4r)

• B doubles (2B) → radius halves (r/2)

SPEED & KINETIC ENERGY
Magnetic force is always ⟂ to velocity → does zero work → ΔKE = 0 → speed is constant
"The magnetic force can bend the path but cannot change the speed."

⚠️ Common student mistake (from lecture): "Acceleration = 0 because speed is constant." WRONG! There IS acceleration — it's centripetal (v²/r), which changes direction, not speed. Acceleration has two aspects: tangential (changes speed) and centripetal/radial (bends path).

L4Tangential vs Centripetal Acceleration

TWO COMPONENTS OF ACCELERATION
Tangential acceleration (aₜ): changes the magnitude of velocity (speeds up or slows down). Force is parallel or anti-parallel to v.
Centripetal/radial acceleration (aᶜ): changes the direction of velocity (bends the path). Force is perpendicular to v. Formula: aᶜ = v²/r

BECAUSE THEY'RE PERPENDICULAR
These two components are independent — you can study them separately. This is why Physics 1 covers straight-line motion first (tangential), then circular motion (centripetal), then combines them.

FOR MAGNETIC FORCE SPECIFICALLY
Magnetic force is always ⟂ to velocity → only centripetal component → aₜ = 0 → constant speed → circular path

🧠 From lecture: "To say the magnetic force is perpendicular to velocity is to say it does no work. Perpendicular forces change direction but not speed."

L5Finding B = 0 Between Two Parallel Wires

SETUP
Two parallel wires 40 cm apart. I₁ = 25 A, I₂ = 75 A. Find where net B = 0 along the line between them.

METHOD
1. Use RHR to find B direction from each wire at various regions (left of both, between, right of both)
2. For B = 0: need B₁ and B₂ equal and opposite
3. From B = μ₀I / (2πr), equal B requires: I₁/r₁ = I₂/r₂

SOLUTION
Since I₂ = 3 × I₁, we need r₂ = 3 × r₁ (three times farther from the stronger wire)
Point must be between the wires where fields oppose. With r₁ + r₂ = 0.4 m and r₂ = 3r₁:
4r₁ = 0.4 → r₁ = 0.1 m (10 cm from I₁, 30 cm from I₂)

KEY INSIGHT
The zero point is always closer to the weaker current — the stronger wire's field needs more distance to weaken enough to match.

L6Alpha Particle in Magnetic Field (Worked Example)

GIVEN
Alpha particle: 2 protons + 2 neutrons
q = 2 × 1.6×10⁻¹⁹ = 3.2×10⁻¹⁹ C
Mass given in problem
B = 1.1 T, enters perpendicular to field

FIND RADIUS
Use r = mv / (|q|B)
Plug in mass, velocity, charge, B → calculate r
Diameter = 2r — read the problem carefully, sometimes they ask for diameter not radius!

FIND DIRECTION OF B
Use RHR: face v direction, force must point toward center of circle (centripetal).
Fingers must match B. Determine if B is into or out of page.

SPEED & KINETIC ENERGY
Speed: constant (magnetic force ⟂ velocity)
ΔKE = 0 (no work done by magnetic force)

ACCELERATION
NOT zero! It's centripetal: a = v²/r
Direction: toward center of circular path

⚠️ Lecture trap: "What effect does B have on speed?" Students say "it accelerates it" — wrong framing. B changes DIRECTION only. Speed stays constant. But there IS acceleration (centripetal). The wrong answer is a = 0.

PHYS 1120 — EXAM 2 REVIEW