⚡ Quick Revision

Last-minute revision in 60 minutes. Flashcards + Formula dump + Memory tricks

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How to Use This Page

Night before exam: Read through all sections once (60 min)
Morning of exam: Formula dump + Flashcards (30 min)
Last 5 min before exam: Common mistakes section

Interactive Flashcards (Click to Flip)

Test your understanding. Click each card to reveal the answer.

Q: Why doesn't magnetic force do work?

A: Force is always perpendicular to velocity (F ⊥ v)

W = F⃗·ds⃗ = 0

No work → No change in KE → Speed remains constant

Q: Formula for radius of circular path?

A: r = mv/(qB) = p/(qB)

Also: r = √(2mK)/(qB)

Key: r ∝ momentum

Q: Why is cyclotron frequency independent of velocity?

A: T = 2πr/v

Substitute r = mv/(qB):

T = 2πm/(qB) ✓

v cancels out!

Q: Biot-Savart vs Ampere's Law - when to use?

Biot-Savart: Any geometry, finite wire, arc

Ampere: High symmetry (infinite wire, solenoid, toroid)

Q: Field inside solenoid?

A: B = μ₀nI

n = N/L (turns per unit length)

Uniform inside, ~0 outside

Q: Parallel currents attract or repel?

Same direction: Attract

Opposite direction: Repel

F/L = (μ₀I₁I₂)/(2πd)

Q: Galvanometer to ammeter - need high or low resistance?

Ammeter: LOW resistance shunt in PARALLEL

S = I_gR/(I-I_g)

Voltmeter: HIGH resistance in SERIES

Q: Can magnetic field accelerate stationary charge?

NO!

F = qvB

If v = 0, then F = 0

Magnetic force acts only on MOVING charges

Q: Why radial field in galvanometer?

A: Ensures B ⊥ coil plane always

Makes torque constant at all positions

τ = NIAB (sin 90° = 1 always)

Click any card to flip. Practice until you can answer all instantly.

Complete Formula Sheet

1. Force & Motion

F⃗ = q(E⃗ + v⃗ × B⃗) — Lorentz Force

F = qvB sin θ — Magnetic force magnitude

r = mv/(qB) = p/(qB) = √(2mK)/(qB) — Radius

T = 2πm/(qB) — Time period

f = qB/(2πm) — Cyclotron frequency

ω = qB/m — Angular frequency

Pitch = v∥T = (v cos θ) × 2πm/(qB) — Helix

2. Magnetic Field Sources

dB⃗ = (μ₀/4π) × (I dl⃗ × r̂)/r² — Biot-Savart Law

B = (μ₀I)/(2πr) — Straight wire

B = (μ₀NI)/(2R) — Circular coil (center)

B = (μ₀NIR²)/[2(R²+x²)^(3/2)] — Circular coil (axis)

B = (μ₀Iθ)/(4πR) — Circular arc (θ in radians)

B = μ₀nI — Solenoid (n = N/L)

B = (μ₀NI)/(2πr) — Toroid

∮ B⃗·dl⃗ = μ₀I_enc — Ampere's Law

3. Force on Conductor

F = BIL sin θ — Force on wire

F⃗ = I(L⃗ × B⃗) — Vector form

F/L = (μ₀I₁I₂)/(2πd) — Between parallel wires

4. Torque & Energy

τ = NIAB sin θ — Torque on loop

τ⃗ = M⃗ × B⃗ — Vector form

M = NIA — Magnetic moment

U = -MB cos θ = -M⃗·B⃗ — Potential energy

W = MB(cos θ₁ - cos θ₂) — Work done

5. Galvanometer & Applications

θ = (NAB/k)I — Deflection

I_s = NAB/k — Current sensitivity

V_s = NAB/(kR) — Voltage sensitivity

S = I_gR/(I-I_g) — Ammeter shunt

R_s = (V/I_g) - R — Voltmeter series R

6. Cyclotron

f = qB/(2πm) — Operating frequency

KE_max = q²B²R²/(2m) — Max energy

v_max = qBR/m — Max velocity

7. Constants

μ₀ = 4π × 10⁻⁷ T·m/A — Permeability of free space

e = 1.6 × 10⁻¹⁹ C — Electron charge

m_e = 9.1 × 10⁻³¹ kg — Electron mass

m_p = 1.67 × 10⁻²⁷ kg — Proton mass

Must-Remember Key Concepts

Core Ideas (Never Forget)

1. Magnetic Force Properties

Acts only on MOVING charges
Always perpendicular to velocity
NEVER does work (W = 0)
Changes direction, NOT speed
KE remains constant

2. Circular Motion

qvB provides centripetal force
r ∝ momentum (p = mv)
T independent of v
Heavier → larger radius
Faster → larger radius

3. Field Direction Rules

Straight wire: Right-hand thumb rule
Circular coil: Right-hand curl rule
Force: Fleming's Left Hand Rule
Negative charge: Reverse direction

4. When to Use Which Law

Biot-Savart: Finite wire, arc, any shape
Ampere: Infinite wire, solenoid, toroid
Symmetry first: Think before calculating

Quick Comparisons

Property	Electric Field	Magnetic Field
Source	Static charges	Moving charges (current)
Acts on	Any charge (static or moving)	Only moving charges
Force direction	Along field lines	Perpendicular to field
Work	Can do work	Cannot do work
Field lines	Start and end on charges	Closed loops (no start/end)
Monopole	Exists (single charge)	Does NOT exist

Common Mistakes (Read 5 Min Before Exam)

❌ Mistake 1: Forgetting sin θ in force formula ▼

Wrong: F = qvB (always)

Right: F = qvB sin θ

Only when perpendicular (θ = 90°): F = qvB

Check question: Does it say "perpendicular"?

❌ Mistake 2: Wrong direction for negative charge ▼

Fleming's rule gives direction for POSITIVE charge

For electron/negative ion: REVERSE the direction

JEE trap: Question asks direction, you apply Fleming's directly for electron → WRONG

❌ Mistake 3: Using R² instead of R in circular coil formula ▼

Wrong: B = μ₀NI/(2R²)

Right: B = μ₀NI/(2R)

Why students make this: Confusing with 1/r² in Coulomb's law

Remember: It's R, not R² for circular coil!

❌ Mistake 4: Unit conversion errors ▼

Common traps:

Current in mA → Convert to A
Distance in cm/mm → Convert to m
Energy in eV → Convert to Joules (1 eV = 1.6 × 10⁻¹⁹ J)
Angle in degrees → Convert to radians for arc formula

Always work in SI units!

❌ Mistake 5: Confusing ammeter and voltmeter conversion ▼

Ammeter: LOW resistance PARALLEL (shunt)

Voltmeter: HIGH resistance SERIES

Memory trick: A-mmeter = pArAllel, Low

V-oltmeter = Series, High (VeSHi)

❌ Mistake 6: Assuming magnetic force changes kinetic energy ▼

Wrong thinking: "Force acts, so KE should change"

Reality: F ⊥ v → W = 0 → KE constant

What changes: Direction of velocity, NOT magnitude

Speed remains constant in pure magnetic field

Memory Tricks & Mnemonics

🎯 Fleming's Left Hand Rule

First = Field (B)

SeCond = Current/Velocity

Thumb = Thrust (Force)

Mnemonic: FBI (Field, B-current-I, Thumb-force)

🎯 r = mv/(qB) - What increases radius?

Heavier → Larger r

Faster → Larger r

More charge → Smaller r

Stronger field → Smaller r

Think: Heavy fast truck hard to turn (big radius)

🎯 Biot-Savart vs Ampere

Biot-Savart = Bad Symmetry (any shape)

Ampere = Awesome symmetry (high symmetry)

If shape is weird → Biot-Savart
If shape is nice (infinite wire, solenoid) → Ampere

🎯 Parallel Currents

Same direction = Attract

Opposite direction = Repel

Mnemonic: SODA (Same→Opposite, Attract→Repel)

🎯 Galvanometer Conversion

Ammeter: Low resistance, Parallel

Voltmeter: High resistance, Series

A-LP (Ammeter Low Parallel)

V-HS (Voltmeter High Series)

🎯 Cyclotron Frequency

f = qB/(2πm)

Independent of velocity!

Remember: "Cycle Time Maintains" (T constant)

Faster → bigger circle → same time

🎯 Solenoid vs Toroid

Solenoid: B = μ₀nI (simple)

Toroid: B = μ₀NI/(2πr) (has 2πr)

Toroid is solenoid bent into circle → gets 2πr term

🎯 Can Magnetic Field Do These?

❌ Accelerate stationary charge (needs v)

❌ Do work (F ⊥ v)

❌ Change speed (KE constant)

✅ Change direction

✅ Provide centripetal force

One-Page Summary (Screenshot This!)

TOP 5 FORMULAS

F = qvB sin θ
r = mv/(qB)
B = μ₀I/(2πr)
B = μ₀nI
τ = NIAB sin θ

TOP 5 CONCEPTS

Magnetic force does NO work
T independent of v
Fleming's LH rule
Parallel currents attract
No magnetic monopoles

TOP 5 MISTAKES

Forget sin θ
Wrong direction for -ve charge
Use R² instead of R
Unit conversion errors
Think B changes KE

EXAM DAY CHECKLIST

☐ Know all 14 formulas
☐ Can apply Fleming's rule instantly
☐ Remember: W = 0 for magnetic force
☐ Know when Biot-Savart vs Ampere
☐ Can convert galvanometer

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Final Words

You've got this! You've learned the concepts, practiced the problems, and understood the patterns. Trust your preparation. In the exam, read carefully, draw diagrams, check units. You're ready. 🚀

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