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Magnetism

Ch. 12Std 11

Easy Overview

Why does a compass needle point north? How do magnets work? And what does electricity have to do with magnetism? This chapter explores magnetism - from the tiny magnetic moments of electrons to the large-scale magnetic fields of Earth and electromagnets. You will learn about the Biot-Savart law (how currents create magnetic fields), Ampere's law (a shortcut for finding magnetic fields in symmetric situations), the force on a current in a magnetic field (the motor effect), and the classification of materials as diamagnetic, paramagnetic, and ferromagnetic. Magnetism and electricity are two sides of the same coin - moving charges create magnetic fields, and magnetic fields exert forces on moving charges. That connection runs through everything from electric motors to MRI machines to the magnetic stripes on credit cards.

Magnetic Field and Its Sources

A magnetic field is a region where a magnetic force is experienced. Represented by B, unit: tesla (T) or gauss (1 T = 10^4 G). Earth's magnetic field is about 0.5 G = 5 x 10^-5 T. A bar magnet has field lines from north to south outside the magnet (south to north inside). Magnetic field lines always form closed loops - they do not start or end anywhere (unlike electric field lines which start and end on charges). There are no magnetic monopoles - a magnetic north pole always comes with a south pole. The sources of magnetic fields are moving charges (currents) and intrinsic magnetic moments of particles (like electron spin).

Biot-Savart Law

The Biot-Savart law gives the magnetic field produced by a tiny current element: dB = (mu_0/4 pi) (I dl x r-hat)/r^2, where mu_0 = 4 pi x 10^-7 T-m/A is the permeability of free space. The direction is given by the right-hand rule (cross product). For a long straight wire: B = mu_0 I / (2 pi r) - the field wraps around the wire in circles. For a circular loop at its center: B = mu_0 I/(2R) (for N turns, multiply by N). For a solenoid: B = mu_0 n I, where n = N/L is turns per unit length. The field is uniform inside a long solenoid and nearly zero outside.

Ampere's Law

Ampere's law: the line integral of B around any closed path equals mu_0 times the current enclosed: closed integral B dot dl = mu_0 I_enclosed. It is the magnetic equivalent of Gauss's law for electricity. For a long straight wire: choosing a circular path of radius r gives B x 2 pi r = mu_0 I, so B = mu_0 I/(2 pi r). For a solenoid: the path encloses nL turns, each carrying I, so B L = mu_0 n L I, giving B = mu_0 n I. For a toroid: B = mu_0 N I/(2 pi r) inside the toroid, zero outside. Ampere's law is only useful for highly symmetric situations.

Force on a Current-Carrying Conductor

A current-carrying wire in a magnetic field experiences a force: F = I L x B, where L is the length vector in the direction of current. Magnitude: F = BIL sin theta, where theta is angle between wire and B. Direction: Fleming's left-hand rule (thumb = force, index finger = field, middle finger = current). Maximum force when wire is perpendicular to B, zero when parallel. This is the motor effect - electric motors use loops of wire in a magnetic field. The torque on a current loop: tau = N I A B sin theta, where A is area of loop, theta is angle between normal to loop and B. This torque drives the rotation in motors and moving coil galvanometers.

Force Between Parallel Currents

Two parallel current-carrying wires exert magnetic forces on each other. Each wire produces a magnetic field that acts on the other wire. The force per unit length: F/L = mu_0 I_1 I_2/(2 pi d), where d is separation. Like currents (same direction) attract. Opposite currents repel. This is how the ampere is defined - one ampere is the current that, flowing in two parallel wires 1 m apart, produces a force of 2 x 10^-7 N per meter. This force is used in high-power circuit breakers - if current gets too high, the magnetic force becomes strong enough to mechanically separate the contacts.

Moving Coil Galvanometer

A moving coil galvanometer (MCG) detects small currents. It has a coil of wire suspended in a radial magnetic field. When current flows, torque acts on the coil: tau = N I A B. A spring provides restoring torque: tau = k phi, where phi is deflection angle. At equilibrium: phi = (N A B / k) I. The deflection is proportional to current. The current sensitivity = phi/I = N A B/k. The voltage sensitivity = phi/V = N A B/(kR). An MCG can be converted to an ammeter by connecting a small shunt resistor in parallel (to bypass most current). It can be converted to a voltmeter by connecting a large series resistor (to limit current through the coil).

Diamagnetism

Diamagnetic materials weakly repel magnetic fields. Water, copper, gold, and bismuth are diamagnetic. When you bring a magnet near them, they create a tiny opposing magnetic field inside - like saying stay away. The effect is super weak - you will not notice it with a fridge magnet. But with a strong enough magnet, you can make a drop of water levitate. Water floats above a magnet because it is diamagnetic. Diamagnetism arises from orbital motion of electrons - an applied field induces currents in electron orbits that oppose the field. All materials have some diamagnetism, but it is usually masked by stronger paramagnetic or ferromagnetic effects.

Paramagnetism and Ferromagnetism

Paramagnetic materials are weakly attracted to magnets. Aluminum, platinum, and oxygen are paramagnetic. Their atoms have unpaired electrons acting as tiny magnets, but randomly oriented. An external magnetic field aligns them slightly - like compass needles. Thermal jiggling keeps knocking them out of alignment - cooling strengthens the effect. Ferromagnetic materials - iron, nickel, cobalt - are strongly attracted and can be permanently magnetized. They have domains - microscopic regions where atomic magnets are already aligned. An external field grows the aligned domains, swallowing misaligned ones. Above Curie temperature, thermal vibrations destroy domain alignment and the material becomes paramagnetic. Iron's Curie temperature: 770 C.

Hysteresis

Hysteresis is the memory of magnetic materials. When you magnetize iron and remove the field, it does not return to zero magnetization - it stays partly magnetized. To demagnetize, you need a field in the opposite direction. The B-H curve (magnetization vs applied field) forms a loop - the hysteresis loop. Materials with wide loops (hard magnets) are used for permanent magnets - they retain magnetization. Materials with narrow loops (soft magnets) are used for transformer cores - they need to magnetize and demagnetize easily. The area of the hysteresis loop represents energy lost as heat per cycle. That is why transformer cores get warm - energy is lost in each AC cycle due to hysteresis.

Key Points

  • •Magnetic field B, unit: tesla (T). Earth's B - 5 x 10^-5 T. Field lines form closed loops.
  • •Biot-Savart law: dB = (mu_0/4 pi) (I dl x r-hat)/r^2. mu_0 = 4 pi x 10^-7 T-m/A.
  • •Long straight wire: B = mu_0 I/(2 pi r). Circular loop center: B = mu_0 I/(2R).
  • •Solenoid: B = mu_0 n I inside, nearly zero outside. n = N/L = turns per unit length.
  • •Ampere's law: closed integral B dot dl = mu_0 I_enclosed. For symmetric situations only.
  • •Force on a conductor: F = I L x B. F = BIL sin theta. Fleming's left-hand rule for direction.
  • •Force between parallel wires: F/L = mu_0 I_1 I_2/(2 pi d). Like currents attract, opposites repel.
  • •Moving coil galvanometer: phi = (NAB/k) I. Converts to ammeter with shunt, voltmeter with series resistor.
  • •Diamagnetic: weakly repel (water, Cu). Paramagnetic: weakly attract (Al, Pt).
  • •Ferromagnetic: strongly attracted (Fe, Ni, Co). Have domains. Above Curie temperature ? paramagnetic.
  • •Hysteresis: B-H loop area = energy lost per cycle. Hard magnets (wide loop) for permanent magnets.
  • •Soft magnets (narrow loop) for transformer cores - magnetize/demagnetize easily.
  • •There are no magnetic monopoles - north pole always paired with south pole.

Practice Questions

  • State Biot-Savart law. Use it to find magnetic field at center of a circular current loop.
  • State Ampere's law. Find magnetic field inside a solenoid and a toroid using it.
  • Derive the expression for force between two parallel current-carrying conductors.
  • Explain working of a moving coil galvanometer. How is it converted into an ammeter and voltmeter?
  • A circular coil of radius 10 cm, 100 turns, carries 5 A. Find magnetic field at its center.
  • Distinguish between diamagnetic, paramagnetic, and ferromagnetic materials with examples.
  • Explain the domain theory of ferromagnetism. What is Curie temperature?
  • What is hysteresis? Draw and explain B-H curve for a ferromagnetic material.
  • Two long parallel wires 5 cm apart carry currents 10 A and 15 A in same direction. Find force per unit length on each.
  • A galvanometer of resistance 100 O gives full-scale deflection for 1 mA. Convert it to (a) 0-1 A ammeter (b) 0-10 V voltmeter.