Magnetic Effects of Current & Magnetism
Practice JEE Main Magnetic Effects of Current & Magnetism PYQs. Biot-Savart law, cyclotron frequency, magnetic dipole moment & step-by-step solutions.
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🎯 High-Yield Syllabus Breakdown
These high-frequency concepts account for over 90% of all questions asked in Magnetic Effects of Current & Magnetism:
- Biot-Savart Law in Vector Form dB = (μ₀/4π) I (dl × r) / r³
- Ampere’s Circuital Law & Solenoid Field B = μ₀ n I
- Magnetic Force on Moving Charge F = q(v × B) & Helical Motion r = mv/(qB)
- Force between Parallel Wires F/L = μ₀ I₁ I₂ / (2π d) (Parallel attract)
- Magnetic Dipole Moment M = N I A and Torque τ = M × B
⚡ Essential Formulas & Speed Shortcuts
Formulas and time-saving shortcuts to solve Magnetism questions in under 45 seconds:
Axis to Center Field Ratio for Loop: B_axis / B_center = [R² / (R² + x²)]^(3/2). For x = R, ratio = 1/(2√2).
Cyclotron Frequency: f = qB / (2πm) is independent of orbit radius and particle speed.
Magnetic Susceptibility: Diamagnetic χ < 0; Paramagnetic χ > 0 and χ ∝ 1/T (Curie’s Law).
📖 Sample Solved Exam Questions
Preview authentic questions from this chapter with full step-by-step solutions:
💡 View Step-by-Step Solution & Answer
Correct Answer: m v / (q B)
- Step 1: The magnetic Lorentz force provides the necessary centripetal force: q v B sin 90° = m v² / r.
- Step 2: Simplify: q v B = m v² / r.
- Step 3: Cancel one velocity v from both sides: q B = m v / r.
- Step 4: Rearrange for radius: r = m v / (q B) = p / (q B).
⚡ Speed Tip: Radius in magnetic field: r = mv / (qB) = p / (qB) = √(2mK) / (qB).
💡 View Step-by-Step Solution & Answer
Correct Answer: B₀ / (2√2)
- Step 1: Magnetic field at center of circular loop: B₀ = μ₀ I / (2R).
- Step 2: Field on axis at distance x: B_axis = μ₀ I R² / [2 (R² + x²)^(3/2)].
- Step 3: For x = R: (R² + R²)^(3/2) = (2R²)^(3/2) = 2√2 R³.
- Step 4: B_axis = [μ₀ I R²] / [2 × 2√2 R³] = [μ₀ I / (2R)] × (1 / 2√2) = B₀ / (2√2).
⚡ Speed Tip: Axis field ratio formula: B_axis / B_center = [R² / (R² + x²)]^(3/2). For x = R, ratio = (1/2)^(3/2) = 1/(2√2).
💡 View Step-by-Step Solution & Answer
Correct Answer: Attractive, μ₀ I₁ I₂ / (2π d)
- Step 1: Magnetic field produced by wire 1 at the location of wire 2 is B₁ = μ₀ I₁ / (2π d).
- Step 2: Magnetic force on length L of wire 2 carrying current I₂ in field B₁ is F = I₂ L B₁.
- Step 3: Force per unit length: F / L = I₂ B₁ = μ₀ I₁ I₂ / (2π d).
- Step 4: By right-hand palm rule, currents in the same direction attract each other. Hence: Attractive, μ₀ I₁ I₂ / (2π d).
⚡ Speed Tip: Parallel currents attract, anti-parallel currents repel. Force per unit length = μ₀ I₁ I₂ / (2πd).
❓ Frequently Asked Questions (FAQs)
Why do parallel currents attract while anti-parallel currents repel?
By the right-hand rule, each wire produces a magnetic field that exerts a Lorentz force directed toward the other wire for parallel currents.