NCERT Solutions for Class 12 Physics Chapter 4 Moving Charges and Magnetism
NCERT Solutions for Class 12 Physics Chapter 4 Moving Charges and Magnetism provides comprehensive notes, important formulas, derivations, and step-by-step solutions covering Lorentz force, Biot-Savart law, Ampere's circuital law, solenoid, force between current-carrying conductors, and moving coil galvanometer.
Overview of Topics & Subtopics (Click to Jump)
1. Magnetic Force, Lorentz Force & Motion in Magnetic Field
Short Note:
• Lorentz Force: Total force experienced by a charge q moving with velocity v in region with both electric (E) and magnetic (B) fields: F = q(E + v × B).
• Magnetic Force: F_m = q(v × B) = q v B sin θ. Magnetic force acts perpendicular to both velocity and magnetic field, so it does no work on the charge.
• Motion in Uniform Magnetic Field:
- Perpendicular Entry (θ = 90°): Charge follows a circular path. Radius r = (m v) / (q B); Time period T = (2π m) / (q B) (independent of v and r).
- Oblique Entry (0° < θ < 90°): Charge follows a helical path with pitch p = v_parallel × T = (2π m v cos θ) / (q B).
2. Biot-Savart Law & Ampere's Circuital Law
Short Note:
• Biot-Savart Law: Magnetic field dB produced by a current element I dl at distance r is: dB = (μ₀ / 4π) × (I dl sin θ / r²), where μ₀ = 4π × 10⁻⁷ T·m/A.
• Applications of Biot-Savart Law:
- Center of Circular Current Loop (radius R, N turns): B = (μ₀ N I) / (2 R).
- Axis of Circular Loop at distance x: B = (μ₀ N I R²) / [2(R² + x²)^(3/2)].
• Ampere's Circuital Law: The line integral of magnetic field B along any closed loop equals μ₀ times net current enclosed: ∮ B · dl = μ₀ I_enclosed.
- Infinitely Long Straight Wire: B = (μ₀ I) / (2π r).
3. Solenoid & Force Between Parallel Current-Carrying Conductors
Short Note:
• Magnetic Field of Long Solenoid: Inside a long solenoid with n turns per unit length carrying current I: B = μ₀ n I (uniform field along the axis; field outside is zero).
• Force on a Current-Carrying Conductor: A straight conductor of length L carrying current I in magnetic field B experiences force: F = I (L × B) = I L B sin θ.
• Force Between Two Parallel Current-Carrying Wires: Force per unit length between two long parallel conductors separated by distance d carrying currents I₁ and I₂:
- Formula: f = F / L = (μ₀ I₁ I₂) / (2π d).
- Nature of Force: Currents in same direction attract; currents in opposite directions repel.
• Definition of 1 Ampere: Constant current which, when flowing through two parallel conductors of infinite length placed 1 meter apart in vacuum, produces force of 2 × 10⁻⁷ N/m per unit length.
4. Torque on Current Loop & Moving Coil Galvanometer
Short Note:
• Magnetic Dipole Moment of Loop (m): m = N I A (vector normal to plane of loop). SI unit is A·m² or J/T.
• Torque on Current Loop: When placed in uniform magnetic field: τ = m × B = N I A B sin θ.
• Moving Coil Galvanometer (MCG): Instrument used to detect and measure small currents.
- Working Principle: Torque acts on current-carrying coil placed in radial magnetic field: τ_deflecting = N I A B.
- Restoring Torque: τ_restoring = k θ => Deflection θ = (N A B / k) × I.
- Current Sensitivity (S_i): Deflection per unit current: S_i = θ / I = (N A B) / k.
- Voltage Sensitivity (S_v): Deflection per unit voltage: S_v = θ / V = (N A B) / (k R).
• Conversion of Galvanometer:
- Into Ammeter: Connect a small resistance (Shunt, S) in parallel: S = (I_g G) / (I - I_g).
- Into Voltmeter: Connect a high resistance (R) in series: R = (V / I_g) - G.
Intext & Conceptual Questions
• Purpose: A radial magnetic field ensures that the magnetic field lines are always parallel to the plane of the coil (θ = 90° between normal to coil plane and magnetic field) regardless of coil rotation. This keeps deflecting torque maximum and constant (τ = N I A B), leading to a linear scale where deflection is directly proportional to current (θ ∝ I).
• Production: It is produced by using concave pole pieces of a permanent magnet along with a soft iron core placed at the center of the coil.
• Static charges interact via electrostatic forces described by Coulomb's Law, where like charges repel each other.
• Parallel current-carrying wires interact via magnetic forces. Wire 1 produces a magnetic field at Wire 2 given by Right-Hand Thumb Rule. Applying Fleming's Left-Hand Rule to Wire 2 shows that the magnetic force points toward Wire 1. By symmetry, Wire 1 is also pulled toward Wire 2. Thus, parallel currents flowing in the same direction exert mutual attractive magnetic forces.
Textbook Chapter End Exercise Questions
Given:
• Number of turns (N) = 100
• Radius of coil (R) = 8.0 cm = 0.08 m
• Current (I) = 0.40 A
• Permittivity constant (μ₀) = 4π × 10⁻⁷ T·m/A
Formula for magnetic field at center of circular coil:
B = (μ₀ N I) / (2 R)
Calculation:
B = (4π × 10⁻⁷ × 100 × 0.40) / (2 × 0.08)
B = (4 × 3.1416 × 10⁻⁷ × 40) / 0.16
B = (502.65 × 10⁻⁷) / 0.16 = 3.14 × 10⁻⁴ T
The magnitude of the magnetic field at the centre of the coil is 3.14 × 10⁻⁴ T.
| Feature | Conversion to Ammeter | Conversion to Voltmeter |
|---|---|---|
| Added Resistance | Very small resistance (Shunt, S). | Very high resistance (R). |
| Connection Type | Connected in parallel with coil. | Connected in series with coil. |
| Formula | S = (I_g G) / (I - I_g) | R = (V / I_g) - G |
| Circuit Connection | Connected in series in main circuit. | Connected in parallel across component. |
| Ideal Value | Ideal Ammeter resistance = 0. | Ideal Voltmeter resistance = ∞. |
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