Magnetism & Moving Charges

Concept Core

Magnetic force, field sources, and moving charge circular motion.

Magnetic Force on Moving Charge (Lorentz Force)

A charge q moving with velocity v in magnetic field B experiences:

F = qv × B |F| = qvB sinθ

θ = angle between v and B. F is perpendicular to both v and B (use right-hand rule for positive charge).

Key: Magnetic force does NO work on a moving charge (F ⊥ v always). It changes direction but not speed.

Circular Motion in Magnetic Field

When v ⊥ B, the charge moves in a circle:

r = mv/(qB) = momentum/(qB) T = 2πm/(qB) = 2πr/v f = qB/(2πm)

Radius proportional to momentum. Period independent of speed (for non-relativistic). Faster particle → larger circle.

Force on Current-Carrying Conductor

F = IL × B |F| = BIL sinθ

L = length of conductor. θ = angle between current direction and B.

F = 0 when current is parallel to B (θ=0).

F is maximum when current ⊥ B (θ=90°).

Biot-Savart Law

Magnetic field due to a small current element:

dB = μ₀/4π × IdL sinθ/r² For long straight wire: B = μ₀I/(2πr) For circular loop at centre: B = μ₀I/(2R)

μ₀ = 4π×10⁻⁷ T·m/A (permeability of free space)

Ampere's Circuital Law

∮B·dL = μ₀ I_enclosed

For a long solenoid: B = μ₀nI (n = turns per unit length)

For a toroid: B = μ₀nI (n = N/2πr, N = total turns)

Outside a solenoid: B = 0

Moving Coil Galvanometer & Its Conversions

Deflection: θ = NIAB/(k) where k = restoring constant.

To ammeter: add low resistance (shunt) in parallel. S = Ig×G/(I−Ig)

To voltmeter: add high resistance in series. R = V/Ig − G

Formula Vault

Magnetism formulas — force, field, and instruments.

Lorentz Force

F = qvB sinθ

θ = angle v makes with B

Circular Motion Radius

r = mv/(qB)

Proportional to momentum

Cyclotron Period

T = 2πm/(qB)

Independent of speed

Force on Conductor

F = BIL sinθ

L = wire length; θ = angle to B

Straight Wire Field

B = μ₀I/(2πr)

At perpendicular distance r

Circular Loop at Centre

B = μ₀I/(2R)

R = radius of loop

Solenoid

B = μ₀nI

n = turns per unit length

Torque on Current Loop

τ = NIAB sinθ

N turns; A = area; θ = angle to B

Shunt (Galvanometer→Ammeter)

S = IgG/(I−Ig)

Ig = galvanometer full-scale current

Series R (→Voltmeter)

R = V/Ig − G

G = galvanometer resistance

Worked Examples

5 problems — Lorentz force, circular motion, wire field, solenoid, galvanometer.

EasyForce on a proton moving at 10⁶ m/s in B = 0.5 T (v ⊥ B)▾

A proton (q = 1.6×10⁻¹⁹ C) moves at 10⁶ m/s perpendicular to B = 0.5 T. Find the magnetic force.

F = qvB sinθ = qvB (since θ=90°, sin90°=1)

F = 1.6×10⁻¹⁹ × 10⁶ × 0.5 = 8×10⁻¹⁴ N

✓ F = 8×10⁻¹⁴ N

EasyFind radius of circular path for electron in B=0.01T, v=10⁷ m/s▾

An electron (m=9.1×10⁻³¹ kg, q=1.6×10⁻¹⁹ C) moves at 10⁷ m/s perpendicular to B=0.01 T. Find the radius.

r = mv/(qB) = (9.1×10⁻³¹ × 10⁷)/(1.6×10⁻¹⁹ × 0.01)

= 9.1×10⁻²⁴ / 1.6×10⁻²¹ = 5.69×10⁻³ m ≈ 5.7 mm

✓ r = 5.7 mm

MediumField at 10 cm from a long wire carrying 5 A▾

Find the magnetic field at 10 cm from a long straight wire carrying 5 A. (μ₀ = 4π×10⁻⁷ T·m/A)

B = μ₀I/(2πr) = (4π×10⁻⁷ × 5)/(2π × 0.1)

= (4π×10⁻⁷ × 5)/(2π × 0.1) = (20π×10⁻⁷)/(0.2π) = 10⁻⁵ T = 10 μT

✓ B = 10 μT

EAPCET LevelConvert galvanometer (G=50Ω, Ig=1mA) to ammeter reading 5A▾

A galvanometer has G=50Ω and full-scale deflection at Ig=1 mA. Find the shunt resistance to make it read 5 A.

Shunt S = Ig × G / (I − Ig) = (1×10⁻³ × 50) / (5 − 1×10⁻³)

= 0.05 / 4.999 ≈ 0.01 Ω = 10 mΩ

✓ Shunt S ≈ 0.01 Ω

Trap QuestionMagnetic force does work on a moving charge — True or False?▾

A student claims that since magnetic force deflects a moving charge, it does work on it and speeds it up. Evaluate.

The trap: Magnetic force is always perpendicular to velocity (F = qv×B → F ⊥ v).

Work = F·d = F d cosθ. Since θ = 90° always, cos90° = 0 → W = 0.

Therefore magnetic force does NO work. The charge's speed remains constant.

Only the direction changes (circular motion). A magnetic field cannot speed up or slow down a charge.

✓ False — magnetic force is always ⊥ to velocity, so W = 0; speed is unchanged

Mistake DNA

4 magnetism errors from EAPCET distractor analysis.

⚡

Magnetic Force Does Work: Confusing Direction Change with Speed Change

Magnetic force changes the direction of velocity, not its magnitude. No work is done.

❌ Wrong

B field deflects charge → charge speeds up ✗ (work = 0; speed constant)

✓ Correct

F ⊥ v always ✓ W = F·v = 0 ✓ Only direction changes; speed stays constant ✓

In circular motion under B: centripetal force (magnetic) is perpendicular to motion. Speed stays constant throughout. Only a tangential force can change speed.

🔄

Right-Hand Rule: Curling Fingers in the Wrong Direction

For current in a straight wire: use right-hand rule — thumb points along current, fingers curl in direction of B field circles.

❌ Wrong

Current upward: B circles clockwise when viewed from above ✗

✓ Correct

Thumb = current direction ✓ Fingers curl = B direction ✓ Current up → B circles counterclockwise (from above)

Point thumb in direction of current (conventional, +charge direction), curl fingers — they show the direction of circular magnetic field lines around the wire.

🔢

Radius of Circular Motion: r = qB/mv instead of mv/(qB)

The formula r = mv/(qB) is often inverted. A larger mass/speed gives larger radius, which the correct formula shows.

❌ Wrong

r = qB/(mv) ✗ → heavier particle: smaller radius (wrong!)

✓ Correct

r = mv/(qB) ✓ Heavier/faster → larger r ✓ Stronger B → smaller r ✓

Derive from qvB = mv²/r: cancelling v → r = mv/(qB). Momentum mv is in numerator, charge q and field B are in denominator.

📻

Solenoid: Forgetting B = 0 Outside

A solenoid creates a uniform B inside. Outside the solenoid, the field is negligibly zero (unlike a bar magnet).

❌ Wrong

Outside a long solenoid: B = μ₀nI/2 or similar ✗

✓ Correct

Outside a long solenoid: B ≈ 0 ✓ Inside: B = μ₀nI ✓ Field confined inside

A long solenoid is like an ideal magnet — field is uniform inside, nearly zero outside. This is why solenoids are used to create controlled, contained magnetic fields.

Chapter Intelligence

Magnetism connects to Current Electricity and leads to EMI & AC Circuits.

EAPCET Weightage (2019–2024)

Force on charge/conductor in B

Circular motion in magnetic field

Biot-Savart (wire, loop)

Solenoid B = μ₀nI

Galvanometer conversions

High-Yield PYQ Patterns

F = qvB sinθ force calculationRadius of circular motion in BB at distance from long wireConvert galvanometer to ammeterSolenoid: B = μ₀nI numericalTorque on current loop in field

Exam Strategy

Direction of force: use F = qv×B. For positive charge, use right-hand rule: fingers point along v, curl toward B — thumb points along F. For negative charge, reverse.
Circular motion in B: r = mv/(qB). Heavier/faster particles trace bigger circles. Period T = 2πm/(qB) is independent of speed — this is the basis of the cyclotron.
Galvanometer to ammeter: shunt S (small, parallel). To voltmeter: series R (large). Both use Ig = full-scale current of galvanometer.
Magnetic force does zero work — this is a conceptual question that appears every few years. Force is perpendicular to velocity → W = 0 → speed constant.

Concept Core

Formula Vault

Worked Examples

Mistake DNA

Chapter Intelligence

💡 Suggestions & Feedback

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