Class 12th Handwritten Physics Notes - Magnetic Effect of Currents

Class 12 CBSE Physics Chapter: Magnetic Effects of Current as per the latest CBSE syllabus:

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Magnetic Effects of Current

1. Introduction

• Electric current produces a magnetic field.

• This magnetic field can exert a force on magnets and other current-carrying conductors.

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2. Oersted’s Experiment

• Observation: When current flows through a wire, it deflects a nearby magnetic compass needle.

• Conclusion: A current-carrying conductor produces a magnetic field around it.

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3. Magnetic Field Due to a Current

(a) Magnetic Field due to a Straight Current-Carrying Conductor

• The field lines are concentric circles centered on the wire.

• Direction: Given by the Right-Hand Thumb Rule.

• Magnitude at a distance r from a long straight wire:

  $$B = \frac{\mu_0 I}{2\pi r}$$

  Where:
  $\mu_0 = 4\pi \times 10^{-7} \, \text{T·m/A}$ (permeability of free space)
  $I$ = current, $r$ = radial distance

(b) Magnetic Field due to a Circular Loop

• At the center of the loop:

  $$B = \frac{\mu_0 I}{2R}$$

  For a coil with N turns:

  $$B = \frac{\mu_0 NI}{2R}$$

  (R = radius of the loop)

(c) Magnetic Field inside a Solenoid

• A solenoid is a coil with many loops.

• The field inside is uniform and strong.

• $$B = \mu_0 n I$$

  Where: $n = \frac{N}{L}$ (number of turns per unit length)

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4. Ampere’s Circuital Law

• States: The line integral of magnetic field B around a closed loop equals $\mu_0 \times$ net current enclosed.

$$\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enclosed}}$$

• Application: Used to derive field due to an infinite wire, solenoid, toroid.

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5. Force on a Moving Charge in a Magnetic Field (Lorentz Force)

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

$$\vec{F} = q(\vec{v} \times \vec{B})$$

• Magnitude:

$$F = qvB\sin\theta$$

• Direction: Perpendicular to both v and B (Right-Hand Rule)

• If θ = 0° or 180°, force = 0 (no deflection)

• Path: Circular if motion is perpendicular

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6. Motion of a Charged Particle in a Magnetic Field

• Circular path:

  $$\text{Centripetal force} = \text{Magnetic force} \Rightarrow \frac{mv^2}{r} = qvB \Rightarrow r = \frac{mv}{qB}$$

• Cyclotron frequency (angular frequency):

  $$\omega = \frac{qB}{m}$$

• Time period:

  $$T = \frac{2\pi m}{qB}$$

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7. Force on a Current-Carrying Conductor

• $$\vec{F} = I (\vec{L} \times \vec{B})$$

  Where:
  $L$ is the length vector in direction of current,
  $B$ is magnetic field

• On a straight conductor of length L in field B:

  $$F = ILB\sin\theta$$

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8. Torque on a Current Loop in Magnetic Field

• Magnetic dipole moment:

  $$\vec{m} = NIA\hat{n}$$

  (A = area vector, N = number of turns)

• Torque:

  $$\vec{\tau} = \vec{m} \times \vec{B}$$

• Potential energy:

  $$U = -\vec{m} \cdot \vec{B}$$

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9. Moving Coil Galvanometer

• Device to detect and measure small currents.

• Principle: Torque on a coil in a magnetic field.

• Torque:

  $$\tau = NIAB\sin\theta$$

• For radial field: $\theta = 90^\circ$, so:

  $$\tau = NIAB$$

• Deflection $\theta \propto I$

• Sensitivity: Increased by using:

  • Strong magnetic field

  • Large area

  • More turns

  • Low torsional constant spring

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10. Conversion of Galvanometer

(a) To Ammeter (Measures Current)

• Add a low resistance shunt parallel to galvanometer.

• Current divides between G and shunt.

• Shunt value:

  $$S = \frac{I_g R_g}{I - I_g}$$

  Where:
  $I_g$ = full-scale deflection current,
  $R_g$ = galvanometer resistance

(b) To Voltmeter (Measures Voltage)

• Add a high resistance in series.

• Total resistance:

  $$R = \frac{V}{I_g} - R_g$$

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Important Laws and Rules

• Right-Hand Thumb Rule: Thumb → current, curled fingers → magnetic field direction.

• Fleming’s Left-Hand Rule: Used to find direction of force on conductor in magnetic field.

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