Overview
This lecture covers the complete chapter "Moving Charges and Magnetism" (Class 12 Physics), including all key concepts, definitions, derivations, formulas, and important numericals, focusing on easy explanations and exam-relevant content.
Magnetic Field and Biot-Savart Law
- Magnetic field is the space around a magnet where its effect can be felt; it is a vector quantity denoted by B (SI unit: Tesla).
- The Biot-Savart Law gives the magnetic field produced by a small current element:
dB = (μ₀/4π) × (I dl × sinθ) / r² (scalar),
dB (vector) = (μ₀/4π) × (I dl × r̂) / r²
- Right-hand rule is used to find the direction: thumb in current's direction, fingers curl in magnetic field direction.
Special Cases and Examples for Current-Carrying Conductors
- Magnetic field is zero along the axis of a straight wire (θ = 0° or 180°).
- Magnetic field is maximum at points perpendicular to the wire (θ = 90°).
- For an infinite straight wire:
B = (μ₀ I) / (2π r)
- For a finite wire:
B = (μ₀ I) / (4π r) × (sinθ₁ + sinθ₂)
- Right-hand thumb rule and slap rule help to find magnetic field direction around wires.
Magnetic Field Due to a Circular Loop and Coil
- At the center of a single-turn loop:
B = (μ₀ I) / (2R)
- For n turns:
B = (μ₀ n I) / (2R)
- For a point on the axis of a loop:
B = (μ₀ n I R²) / [2(R² + x²)^(3/2)]
- Direction found using right-hand rule; current’s direction gives magnetic field’s direction.
Ampere's Circuital Law and Applications
- Ampere's Law: The line integral of B·dl around a closed loop equals μ₀ times the net current enclosed.
∮B·dl = μ₀ I_enclosed
- For a long straight conductor:
B = (μ₀ I) / (2π r)
- For a solid cylindrical wire (radius A):
- Outside (r > A): B ∝ 1/r
- Inside (r < A): B ∝ r
Solenoid
- Magnetic field inside a (long) solenoid:
B = μ₀ n I (n = turns per unit length)
- At ends of solenoid: B = (μ₀ n I) / 2
Force on Moving Charge and Current
- Force on charge in magnetic field:
F = q(v × B) = qvB sinθ
- Direction found by Fleming’s left-hand rule (force, magnetic field, velocity are mutually perpendicular).
- If charge moves parallel to B or is at rest, force is zero; maximum at θ = 90°.
- In a magnetic field, a perpendicular entry leads to a circular path;
- Radius: r = (mv)/(qB)
- Time period: T = (2π m) / (qB)
- Frequency (Cyclotron frequency): f = (qB) / (2π m)
- If entry angle is not 90°, particle follows a helical path; pitch = v_parallel × T.
Force on a Conductor and Between Conductors
- Force on a current-carrying wire in B:
F = I (L × B)
- Two parallel currents:
- Same direction: attract
- Opposite direction: repel
- Force per unit length: F/L = (μ₀ I₁ I₂) / (2π r)
- Definition of 1 ampere is based on the force between two parallel wires.
Torque and Magnetic Dipole Moment
- A current loop behaves as a magnetic dipole, moment m = n I A.
- Torque on loop in B:
τ = m × B = n I A B sinθ
- Maximum torque when θ = 90°.
Moving Coil Galvanometer (MCG), Ammeter, and Voltmeter
- A galvanometer detects and measures small currents based on torque from current in a magnetic field.
- Angular deflection α ∝ current I:
α = (n B A / k) × I
- To convert to ammeter: connect low-resistance shunt (S) in parallel;
S = (I_G × G) / (I - I_G)
- To convert to voltmeter: connect high resistance (R) in series;
R = (V / I_G) - G
- Sensitivity increases with n, B, A, and decreases with k.
Key Terms & Definitions
- Magnetic Field (B) — Region around a magnet where magnetic effects are felt (vector; unit: Tesla).
- Biot-Savart Law — Describes the magnetic field generated by a current element.
- Ampere’s Law — Relates the integrated magnetic field around a closed loop to the current passing through.
- Solenoid — A coil of wire acting as a magnet when carrying current.
- Magnetic Dipole Moment (m) — Product of current, area, and number of turns (nIA).
- Torque (τ) — Rotational effect on a loop in a magnetic field.
- Galvanometer — Device for detecting/measuring small electric currents.
- Ammeter — Measures current; constructed by shunting galvanometer.
- Voltmeter — Measures voltage; constructed by adding high resistance to galvanometer.
- Sensitivity — Deflection per unit current or voltage.
Action Items / Next Steps
- Review all key formulas and derivations, especially Biot-Savart, Ampere’s Law, force on moving charge, and conversion processes for galvanometer.
- Practice numerical problems on magnetic field due to wires, loops, solenoids, and force calculations.
- Memorize right-hand and left-hand rules, key directions, and definitions for exam use.
- Prepare handwritten summaries of all derivations for revision before exams.