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.
1
F = qvB sinθ = qvB (since θ=90°, sin90°=1)
2
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.
1
r = mv/(qB) = (9.1×10⁻³¹ × 10⁷)/(1.6×10⁻¹⁹ × 0.01)
2
= 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)
1
B = μ₀I/(2πr) = (4π×10⁻⁷ × 5)/(2π × 0.1)
2
= (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.
1
Shunt S = Ig × G / (I − Ig) = (1×10⁻³ × 50) / (5 − 1×10⁻³)
2
= 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.
1
The trap: Magnetic force is always perpendicular to velocity (F = qv×B → F ⊥ v).
2
Work = F·d = F d cosθ. Since θ = 90° always, cos90° = 0 → W = 0.
3
Therefore magnetic force does NO work. The charge's speed remains constant.
4
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~8 Circular motion in magnetic field~6 Biot-Savart (wire, loop)~5 Galvanometer conversions~3 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.