"Magnetism and Magnetic Effect of Electric Current"

About

Magnetism and electricity are two sides of the same coin — moving charges produce magnetic fields, and magnetic fields exert forces on moving charges. This chapter covers the magnetic effects of electric current, the laws that govern them, and practical devices like the galvanometer.

Key Concepts

18.1 Magnets and Magnetic Poles

A magnet has two poles — north (N) and south (S):

• Like poles repel; unlike poles attract
• Poles always exist in pairs — magnetic monopoles don't exist
• A freely suspended magnet aligns N-S (Earth's magnetic field)

To identify the north pole: Suspend a magnet freely — the end pointing toward geographical north is the north pole. Or use repulsion with a known magnet (repulsion confirms like poles).

To identify which of two identical iron bars is a magnet: Bring each near the middle of the other. A magnet has poles only at its ends (middle has no strength), but can magnetize an iron bar. The bar that attracts when brought near the middle of the other IS the magnet.

18.2 Magnetic Field Due to Electric Current

Stationary charge: Produces only electric field — NO magnetic field.

Moving charge: Produces BOTH electric and magnetic fields. The magnetic field circles around the path of motion.

In a conductor without applied voltage: Electrons move randomly (thermal motion) — their magnetic fields cancel → net field = 0.

With applied voltage: Electrons drift in a definite direction → net current → net magnetic field is produced.

18.3 Biot-Savart Law

The magnetic field $dB$ due to a current element $Idl$:

$dB=\frac{{\mu }_0}{4\pi }\frac{Idl\sin \theta }{r^2}$

Where ${\mu }_0=4\pi \times 10^{-7}$ T⋅m/A (permeability of free space).

Applications:

18.4 Ampere's Circuital Law

$\oint \vec{B}\cdot d\vec{l}={\mu }_0{I}_{\text{enclosed}}$

Used to find $B$ for symmetric current distributions.

18.5 Force on a Current-Carrying Conductor

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

Magnitude: $F=BIl\sin \theta$

18.6 Force Between Parallel Currents

• Parallel currents in same direction → attract
• Parallel currents in opposite direction → repel

Force per unit length: $F/l=\frac{{\mu }_0{I}_1{I}_2}{2\pi d}$

18.7 Moving Coil Galvanometer

Converts electric current into mechanical deflection. Uses the principle that a current-carrying coil in a magnetic field experiences a torque.

INTEXT QUESTIONS 18.1

Q1. You are given a magnet. How will you locate its north pole?

Ans: Suspend the magnet freely with a thread at its centre. Allow it to rotate freely and come to rest. The end pointing toward geographical north is the north pole. Alternatively, bring a known magnet's north pole near one end — if repulsion occurs, that end is also north (like poles repel).

Q2. You are provided two identical looking iron bars. One is a magnet. Using just these two, how will you identify which is the magnet?

Ans: Bring bar A near the middle of bar B. If bar A is the magnet, it magnetizes bar B and attraction occurs. If bar B is brought near the middle of bar A and there's no attraction, bar A is the magnet (its middle has no poles). The bar that shows attraction when brought near the middle of the other IS the magnet.

Q3. You are given a thread and two bar magnets. Describe a method to identify the polarities of both magnets.

Ans: (1) Suspend magnet 1 using thread at its centre — the end pointing geographic north is its north pole (N₁). (2) Bring N₁ near one end of magnet 2 — if repulsion, that end is also north; if attraction, that end is south. The opposite end has opposite polarity.

INTEXT QUESTIONS 18.2

Q1. What can you say about the field developed by (i) a stationary electron? (ii) a moving electron?

Ans: (i) Stationary electron: Produces only an electric field (radial, inward). No magnetic field is produced.

(ii) Moving electron: Produces BOTH electric and magnetic fields. The magnetic field lines are circular around the path of motion. Stationary charges → only E-field; moving charges → both E and B fields.

Q2. Electrons in a conductor are in constant motion due to thermal energy. Why do they not show magnetism till a potential difference is applied?

Ans: Without potential difference, electrons move randomly in all directions — their individual magnetic fields cancel out, giving zero net field. When a potential difference is applied, electrons gain a net drift velocity in a definite direction. All electrons produce magnetic fields in the same direction → net magnetic field appears.

Terminal Exercise

1. State the properties of magnetic field lines. Draw field lines for a bar magnet.

2. State Biot-Savart law. Derive the expression for magnetic field at the centre of a circular current loop.

3. State Ampere's circuital law. Use it to derive the magnetic field due to: (a) a long straight current-carrying wire, (b) a solenoid.

4. Derive the expression for force on a current-carrying conductor in a magnetic field: $\vec{F}=I(\vec{l}\times \vec{B})$.

5. Two long parallel wires carry currents of 5 A and 10 A in the same direction, separated by 2 cm. Find the force per unit length between them. Is it attractive or repulsive?

6. Explain the principle, construction, and working of a moving coil galvanometer. How can it be converted to (a) an ammeter, (b) a voltmeter?

7. A circular coil of 100 turns, radius 10 cm, carries a current of 5 A. Find the magnetic field at its centre.

8. A straight wire of length 0.5 m carries a current of 10 A and is placed perpendicular to a magnetic field of 0.2 T. Find the force on the wire.

9. Distinguish between diamagnetic, paramagnetic, and ferromagnetic materials with examples.

10. Explain why: (a) a freely suspended magnet aligns N-S, (b) magnetic monopoles do not exist, (c) a current loop behaves like a magnetic dipole.

11. Compare Biot-Savart law with Coulomb's law. State two similarities and two differences.

12. What is the magnetic field at a point 10 cm from a long straight wire carrying 5 A current?

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