Class 12 Physics Moving Charges and Magnetism Notes

4.1 Introduction

Moving charges produce magnetic effects. This chapter explains how electric currents generate magnetic fields, how charges move in a magnetic field, and the interaction between currents and magnets. These concepts form the basis for devices like motors, galvanometers, and electromagnets.

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4.2 Magnetic Force

A charged particle moving in a magnetic field experiences a force known as the Lorentz force:$$\vec{F} = q \vec{v} \times \vec{B}$$F=qv×B

• Direction is given by the right-hand rule.
• Magnitude: $F = qvB\sin\theta$F=qvBsinθ
  • θ = angle between velocity $\vec{v}$v and magnetic field $\vec{B}$B
• Force is perpendicular to both velocity and magnetic field.

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4.3 Motion in a Magnetic Field

• Charged particle in a uniform magnetic field moves in a circular or helical path.
• Radius of circular path:

$$r = \frac{mv}{qB}$$r=qBmv​

• Period of revolution:

$$T = \frac{2\pi m}{qB}$$T=qB2πm​

• Magnetic force does no work; kinetic energy remains constant.

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4.4 Magnetic Field due to a Current Element – Biot–Savart Law

The Biot–Savart Law gives the magnetic field due to a small current element:$$d\vec{B} = \frac{\mu_0}{4\pi} \frac{I d\vec{l} \times \hat{r}}{r^2}$$dB=4πμ0​​r2Idl×r^​

• I = current in the element
• $d\vec{l}$dl = length vector of current element
• r = distance to the point
• μ₀ = permeability of free space

It is used to calculate magnetic fields for wires of different shapes.

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4.5 Magnetic Field on the Axis of a Circular Current Loop

• Magnetic field at the center of a circular loop of radius R carrying current I:

$$B = \frac{\mu_0 I}{2R}$$B=2Rμ0​I​

• Field is along the axis of the loop.
• Superposition can be used for multiple loops (solenoid).

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4.6 Ampere’s Circuital Law

Statement:
The line integral of the magnetic field $\vec{B}$B around a closed loop equals $\mu_0$μ0​ times the net current passing through the loop:$$\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enclosed}}$$∮B⋅dl=μ0​Ienclosed​

• Useful for calculating fields of long straight wires, solenoids, and toroids.

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4.7 The Solenoid

• A solenoid is a long coil of wire carrying current.
• Magnetic field inside a solenoid:

$$B = \mu_0 n I$$B=μ0​nI

• n = number of turns per unit length
• Field outside is nearly zero.
• Solenoids behave like a bar magnet with north and south poles.

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4.8 Force Between Two Parallel Currents – The Ampere

• Two parallel currents exert forces on each other:
  • Attractive if currents flow in the same direction
  • Repulsive if currents flow in opposite directions

Force per unit length:$$F/L = \frac{\mu_0 I_1 I_2}{2\pi d}$$F/L=2πdμ0​I1​I2​​

• Defines ampere, the SI unit of current.

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4.9 Torque on a Current Loop – Magnetic Dipole

• A current-carrying loop in a magnetic field experiences a torque:

$$\tau = n I A B \sin\theta$$τ=nIABsinθ

• n = number of turns, A = area of loop, θ = angle between plane of loop and B
• The loop behaves like a magnetic dipole:

$$\vec{m} = I \vec{A}$$m=IA

• Potential energy of a magnetic dipole:

$$U = -\vec{m} \cdot \vec{B}$$U=−m⋅B

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4.10 The Moving Coil Galvanometer

• A moving coil galvanometer converts electric current into mechanical rotation.
• Key points:
  • Coil is suspended in a uniform magnetic field
  • Torque on the coil is proportional to the current
  • Can measure current or, with modifications, voltage

Applications: Ammeter, Voltmeter