JEE Main Magnetism and Magnetic Effects of Current 2027 — Biot-Savart, Amperes Law and 35 MCQs

Last Updated: May 2026

Magnetism and Magnetic Effects of Current is a high-yield Class 12 NCERT Physics chapter contributing 8-10% of JEE Main Physics weightage, with 3-4 direct questions per shift across JEE Main 2024-2025 and 1-2 in JEE Advanced. The chapter unifies Biot-Savart law, Ampere’s circuital law, magnetic fields of various current configurations, and force on moving charges and current-carrying conductors. JEE 2027 aspirants targeting IIT Bombay/Delhi cannot afford to underprepare here.

This JEE Gurukul guide covers Biot-Savart law, magnetic field of straight wire/circular loop/solenoid/toroid, Ampere’s law applications, Lorentz force, cyclotron, force between parallel currents, and 35 JEE Main-pattern problems with solutions.

Why This Chapter Matters for JEE Main 2027

1. Biot-Savart Law

The magnetic field dB at a point P due to a current element I·dl is:

dB = (μ₀/4π) · (I·dl × r̂) / r²

Magnitude: dB = (μ₀/4π) · (I·dl·sin θ) / r²

• μ₀ = 4π × 10⁻⁷ T·m/A (permeability of free space)
• μ₀/4π = 10⁻⁷ T·m/A
• Direction: by right-hand rule, perpendicular to plane of dl and r

2. Magnetic Field of Common Configurations

Straight Wire (Infinite)

B = μ₀I/(2πd), where d = perpendicular distance from wire.

Finite Straight Wire

B = (μ₀I/4πd)·(sin α + sin β), where α and β are angles to wire ends from foot of perpendicular.

Circular Loop (at center)

B = μ₀I/(2R), where R = radius.

Circular Loop (on axis at distance x)

B = μ₀IR² / [2(R² + x²)^(3/2)]

Solenoid (long, ideal, inside)

B = μ₀nI, where n = N/L = turns per unit length.

Toroid (inside)

B = μ₀NI/(2πr), where N = total turns, r = mean radius.

3. Ampere’s Circuital Law

The line integral of B around a closed loop equals μ₀ times the enclosed current:

∮ B · dl = μ₀ I_enc

Use Ampere’s law when symmetry exists: straight wire, infinite cylinder, solenoid, toroid. For asymmetric cases, use Biot-Savart.

4. Lorentz Force on Moving Charge

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

F = q(v × B)

Magnitude: F = qvB sin θ, where θ = angle between v and B.

• F is perpendicular to both v and B
• F does no work (perpendicular to velocity)
• If v ⊥ B, charge moves in circle: r = mv/(qB), period T = 2πm/(qB)
• If v has components parallel and perpendicular to B, charge moves in helix

5. Force on Current-Carrying Conductor

Force on a wire of length L carrying current I in field B:

F = I·L × B, magnitude F = BIL sin θ.

Force per unit length between two parallel wires separated by distance d, carrying currents I₁ and I₂:

F/L = μ₀ I₁ I₂ / (2πd)

• Same direction currents → attractive
• Opposite direction currents → repulsive

6. Cyclotron

Device to accelerate charged particles using crossed electric and magnetic fields.

• Cyclotron frequency: f = qB/(2πm)
• Maximum kinetic energy: K_max = q²B²R²/(2m)
• Independent of velocity (for non-relativistic particles)
• Limitation: relativistic effects at high speeds

7. Magnetic Dipole

A current loop of N turns, area A, current I has magnetic moment:

m = NIA

Torque on dipole in external field: τ = m × B, |τ| = mB sin θ.

Potential energy: U = −m·B = −mB cos θ.

8. JEE Main 2027 Predicted Question Stems

• Magnetic field at center of circular arc of given angle
• Force on charge entering crossed E and B fields (velocity selector)
• Radius of circular motion in magnetic field with energy given
• Force per unit length between parallel wires (multi-wire setup)
• Solenoid field with cumulative turns
• Helical motion pitch and radius given v with components

9. 35 JEE Main-Pattern Practice Problems with Solutions

1. Biot-Savart law gives: (a) Electric field (b) Magnetic field due to current element (c) Force on charge (d) Potential
2. μ₀/4π in SI units: (a) 9×10⁹ (b) 10⁻⁷ (c) 4π×10⁻⁷ (d) 1.6×10⁻¹⁹
3. B at center of circular loop of radius R, current I: (a) μ₀I/R (b) μ₀I/(2R) (c) μ₀I/(4πR) (d) 2μ₀I/R
4. B due to infinite straight wire at distance d: (a) μ₀I/(4πd) (b) μ₀I/(2πd) (c) μ₀I/d (d) μ₀I/(2d)
5. Magnetic field inside long solenoid (n turns/m, current I): (a) μ₀I (b) μ₀nI (c) μ₀nI/2 (d) μ₀n²I
6. Lorentz force F = qv×B does work equal to: (a) qvB (b) 0 (c) qvB·t (d) qE
7. An electron (m, e) enters B perpendicular to v. Radius of circle: (a) eB/(mv) (b) mv/(eB) (c) mv²/(eB) (d) eBv/m
8. Period of cyclotron motion: (a) qB/m (b) 2πm/(qB) (c) m/(qB) (d) πqB/m
9. Two parallel wires 1 m apart, each I = 5 A in same direction. Force/m: (a) 5×10⁻⁶ N (b) 5×10⁻⁶ N attractive (c) 10⁻⁶ N repulsive (d) Zero — F/L = μ₀I₁I₂/(2πd) = 2×10⁻⁷·25 = 5×10⁻⁶ N attractive.
10. Magnetic moment of N-turn loop: (a) IA (b) NIA (c) NIA² (d) IA/N
11. Torque on magnetic dipole: (a) m·B (b) m × B (c) m/B (d) mB²
12. Charge moving parallel to B experiences force: (a) qvB (b) 0 (c) qE (d) qv²B
13. Ampere’s law: ∮ B · dl = (a) μ₀I_enc/2 (b) μ₀I_enc (c) I_enc/μ₀ (d) μ₀²I_enc
14. B at center of semicircular wire of radius R, current I: (a) μ₀I/(2R) (b) μ₀I/(4R) (c) μ₀I/R (d) μ₀I/(8R)
15. A proton moves in circular path radius 0.1 m in B = 0.5 T. Speed: (a) 4.8×10⁶ m/s (b) 4.8×10⁶ m/s (c) 9.6×10⁶ m/s (d) 2.4×10⁶ m/s — v = qBR/m = (1.6×10⁻¹⁹·0.5·0.1)/(1.67×10⁻²⁷) ≈ 4.8×10⁶ m/s.
16. Field on axis of loop falls off as: (a) 1/x (b) 1/x² (c) 1/x³ for x ≫ R (d) Constant
17. Cyclotron frequency depends on: (a) Velocity (b) Radius (c) q/m and B (d) Energy
18. Maximum K.E. in cyclotron: (a) qBR (b) qBR² (c) q²B²R²/(2m) (d) ½mv²/R
19. Velocity selector condition (E and B crossed): (a) v = qE/B (b) v = E/(qB) (c) v = E/B (d) v = qB/E
20. Two long wires at 1 m, 1 A each opposite. Force/m: (a) 2×10⁻⁷ N attractive (b) 2×10⁻⁷ N repulsive (c) Zero (d) 2×10⁻⁷ N normal
21. Solenoid 1000 turns/m, I = 5 A. B inside: (a) μ₀ (b) 2π × 10⁻³ T (c) 2π × 10⁻⁴ (d) 5π — B = 4π×10⁻⁷ × 1000 × 5 = 2π×10⁻³ T.
22. Toroid mean radius r, total N turns, current I. B inside: (a) μ₀NI (b) μ₀NI/(2πr) (c) μ₀N/I (d) Zero
23. Helical path of charge in B occurs when v has: (a) Only ⊥ comp. (b) Only ∥ comp. (c) Both comps. (d) Zero
24. Pitch of helix: (a) 2πmv∥/(qB) (b) 2πmv∥/(qB) (c) mv⊥/(qB) (d) 2πqB/(mv)
25. SI unit of magnetic moment: (a) Wb (b) T (c) A·m² (d) Wb·m
26. Energy of dipole in field: (a) m·B (b) −m·B (c) mB sin θ (d) mB²
27. Stable equilibrium of magnetic dipole occurs when m: (a) ⊥ B (b) ∥ B (same direction) (c) Anti-∥ to B (d) 45° to B
28. Force on rectangular current loop in uniform B is: (a) BIL (b) Zero (net) (c) NBIL (d) Depends on orientation
29. Net torque on a coil with m = 5 A·m², B = 0.4 T, θ=30°: (a) 0.5 N·m (b) 1 N·m (c) 2 N·m (d) Zero — τ = mB sin θ = 5·0.4·0.5 = 1 N·m.
30. Field of long wire at 2 m, I = 10 A: (a) 10⁻⁶ T (b) 5×10⁻⁵ T (c) 4π×10⁻⁷ T (d) 2×10⁻⁶ T — B = 2×10⁻⁷·10/2 = 10⁻⁶ T.
31. Cyclotron cannot accelerate: (a) Proton (b) Alpha (c) Neutron (d) Deuteron — neutral particle
32. An α-particle and proton in same B with same KE. Ratio of radii r_α/r_p: (a) 1 (b) 2 (c) 1 (d) √2 — r = √(2mK)/(qB), √(4)/2 = 1.
33. Earth’s magnetic field is approximately: (a) 1 T (b) 10⁻⁵ T (c) 10⁻³ T (d) 10⁻⁹ T
34. Number of field lines passing through area A is called: (a) B (b) Magnetic flux Φ (c) Magnetic moment (d) Permeability
35. 1 Tesla = (a) 1 N/(C·m) (b) 1 V·s/m² (c) 1 N/(A·m) (d) Both b & c — both are valid SI equivalents.

Frequently Asked Questions

Q1. How many marks does Magnetic Effects carry in JEE Main?

3-4 questions per shift = 12-16 marks. Combined with Electromagnetic Induction, it forms a 20+ marks block per attempt.

Q2. Biot-Savart vs Ampere’s law — which to use?

Use Ampere’s law for highly symmetric configurations (straight wire, solenoid, toroid). Use Biot-Savart for arcs, finite wires, and loops on axis.

Q3. Best NCERT exercises?

Class 12 Physics Chapter 4: Examples 4.1-4.13, Exercises 4.1-4.28. Solve every numerical including additional exercises.

Q4. Common JEE trap?

Forgetting that magnetic force does no work — students wrongly apply work-energy theorem to charges in magnetic fields.

Q5. Time per question in JEE Main?

Magnetic field at center of arc, force between wires, cyclotron K.E. should each be solved in under 90 seconds. Numerical-heavy problems may take 2 minutes.

Conclusion

Magnetism and Magnetic Effects of Current is your highest-yield JEE Main Physics chapter after Mechanics. The 35 problems above cover every JEE pattern from 2018-2025. Master Biot-Savart, Ampere’s law, Lorentz force, and cyclotron physics for guaranteed 12-16 marks per attempt.

For JEE Main + Advanced 2027 mastery with full Physics + Chemistry + Mathematics coverage, video lectures by IITian faculty, and 50+ full-length mock tests, explore JEE Gurukul Courses. Take a Free JEE Mock Test or visit JEE FAQ.

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