Class 12 Physics - Quick Revision Notes

Chapter: Moving Charges and Magnetism (गतिमान आवेश और चुंबकत्व)

Oersted's Discovery: Electric current flowing through a conductor produces a magnetic field around it.
Magnetic Field ($B$): Measured in Tesla (T) or Weber per meter squared ($Wb/m^2$). CGS unit is Gauss (G). ($1 \text{ Tesla} = 10^4 \text{ Gauss}$).

When a charge $q$ moves with velocity $v$ in a magnetic field $B$, it experiences a force.

Formula: F = q (v x B) or F = qvB sin(θ)
- $F$ = Magnetic Force
- $q$ = Charge
- $v$ = Velocity of charge
- $B$ = Magnetic field intensity
- $θ$ = Angle between velocity vector and magnetic field vector
Special Cases:
- If $\theta = 0^\circ$ or $180^\circ$ (Parallel/Anti-parallel): F = 0 (Minimum Force)
- If $\theta = 90^\circ$ (Perpendicular): F = qvB (Maximum Force)
Direction: Determined by Fleming's Left Hand Rule or Right-Hand Thumb Rule.

Circular Path: When a charged particle enters perpendicularly to a magnetic field ($\theta = 90^\circ$), it moves in a circular path.
- Radius of the path ($r$): r = mv / (qB) or r = p / (qB) (where $p = mv$ is momentum)
- Alternative Formula (in terms of accelerating potential $V$): r = sqrt(2mV) / (qB)
- Time Period ($T$): T = 2πm / (qB)
- Frequency ($f$): f = qB / (2πm)
Helical Path: When a charged particle enters at an angle $\theta$ (other than $0^\circ, 90^\circ, 180^\circ$), its path is a helix.
- Pitch of the helix: Distance moved along the magnetic field in one full rotation. Pitch = (2πm v cosθ) / (qB)

A particle passes undeflected through perpendicular electric ($E$) and magnetic ($B$) fields.
Condition: v = E / B

Definition: A device used to accelerate positively charged particles to high energies.
Working Principle: A charged particle is accelerated repeatedly by an alternating electric field while being made to circle in a magnetic field using strong electromagnets.
Cyclotron Frequency: f = qB / (2πm)
Maximum Kinetic Energy of Ions: E_max = (q^2 B^2 R^2) / (2m) (where $R$ is the radius of the dee)
Note: Cyclotron cannot accelerate uncharged particles (neutrons) and electrons (due to their very small mass, they lose resonance quickly).

It gives the magnetic field $dB$ due to a small current-element $Idl$.

Formula: dB = (μ_0 / 4π) * (I dl sinθ) / r^2
- In vector form: dB = (μ_0 / 4π) * (I (dl x r)) / r^3
- $\mu_0$ = Permeability of free space $= 4\pi \times 10^{-7} \text{ T m A}^{-1}$
Applications:
1. Magnetic Field at the center of a circular current-carrying loop: B = (μ_0 I) / (2R) (For $N$ turns: B = μ_0 N I / (2R))
2. Magnetic Field at an axial point of a circular loop: B = (μ_0 I R^2) / (2 (R^2 + x^2)^(3/2))

Statement: The line integral of magnetic field $B$ around any closed loop is equal to $\mu_0$ times the total current ($I_{enclosed}$) passing through the loop.
Formula: ∫ B . dl = μ_0 * I_enclosed
Applications:
1. Magnetic Field due to an Infinite Long Straight Current-Carrying Wire: B = (μ_0 I) / (2πr)
2. Magnetic Field inside a Long Solenoid: B = μ_0 n I (where $n = N/L$ is the number of turns per unit length)
3. Magnetic Field inside a Toroid: B = μ_0 n I (where $n = N / (2\pi r)$)

Formula: F = I (L x B) or F = I L B sin(θ)
- $L$ = Length of the conductor
- $I$ = Current flowing through it

Force per unit length ($F/L$): F / L = (μ_0 I_1 I_2) / (2πd)
- $d$ = Distance between the two conductors.
Nature of Force:
- Currents in same direction $\rightarrow$ Attract each other.
- Currents in opposite direction $\rightarrow$ Repel each other.
Definition of 1 Ampere: One Ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, placed 1 meter apart in vacuum, produces a force of $2 \times 10^{-7} \text{ N/m}$ between them.

Formula: τ = M x B or τ = N I A B sin(θ)
- $N$ = Number of turns in the coil
- $A$ = Area of the coil
- $M$ = Magnetic Dipole Moment $= N I A$
- $\theta$ = Angle between the normal to the coil and the magnetic field $B$.

Used to detect and measure small electric currents.
Principle: Current-carrying coil placed in a magnetic field experiences a torque.
Equilibrium condition: Deflecting Torque = Restoring Torque
- N I A B = k θ (where $k$ is the torsional constant of the spring)
Current Sensitivity ($I_s$): I_s = θ / I = (N A B) / k
Voltage Sensitivity ($V_s$): V_s = θ / V = (N A B) / (k R)

Galvanometer to Ammeter:
- A low resistance called Shunt ($S$) is connected in parallel with the galvanometer.
- Formula for Shunt: S = (I_g * G) / (I - I_g)
- Effective Resistance of Ammeter: R_A = (G * S) / (G + S)
Galvanometer to Voltmeter:
- A high resistance ($R$) is connected in series with the galvanometer.
- Formula for Series Resistance: R = (V / I_g) - G
- Effective Resistance of Voltmeter: R_V = G + R

All the Best for your MP Board Exams! Prepare well.