Chapter 11 — Magnetic Effects Of Electric Current

Introduction
A magnetic effect of electric current means that an electric current produces a magnetic field in the space around the conductor carrying the current. This is the basis of many devices (motors, electromagnets, speakers).

Oersted's Experiment (setup and procedure)

• Place a small magnetic compass on a table and note that its needle points towards the Earth's magnetic north when no current flows.
• Place a straight, horizontal conducting wire just above the compass needle and connect the wire to a battery through a switch.
• Close the switch so that current flows through the wire. Observe the compass needle.

Observations

• When current flows, the compass needle gets deflected from its original direction. The deflection disappears when the current is switched off.
• If the direction of current in the wire is reversed, the needle deflects in the opposite direction.
• The amount of deflection increases with larger current and decreases if the wire is moved farther from the compass.

Conclusions

• A current-carrying conductor produces a magnetic field around it.
• The magnetic field lines around a long straight conductor are concentric circles centred on the wire.
• The direction of the magnetic field around a straight wire is given by the right-hand thumb rule: if the thumb of the right hand points along the direction of conventional current, the curled fingers show the direction of the magnetic field lines.

Qualitative relations

• Magnetic field strength around a straight conductor increases with the current flowing through it.
• Magnetic field strength decreases with distance from the conductor.

Practical notes
Oersted's discovery linked electricity and magnetism and led to development of electromagnets, electric motors and generators. Simple classroom demonstrations use a compass, a straight wire and a battery to show the effect clearly.

Magnetic field (B) is the region around a magnet, a current-carrying conductor or a changing electric field in which magnetic forces can be detected. At any point the magnetic field has a direction and magnitude. The SI unit of magnetic field (magnetic flux density) is tesla (T).

Magnetic field lines are imaginary continuous curves used to represent the magnetic field. They show both the direction and relative strength of the field. Important features:

• Field line direction: tangent to a field line at any point gives the direction of the magnetic field at that point.
• Line sense: outside a magnet, lines go from the north (N) pole to the south (S) pole; inside the magnet they return from S to N, so lines are closed loops.
• Density: where lines are closer the field is stronger; where they are sparse the field is weaker.
• Never cross: two field lines do not intersect. If they did, the field would have two directions at one point, which is impossible.

Field due to a straight current-carrying conductor:

• Magnetic field lines around a long straight current are concentric circles centered on the wire.
• Direction rule: use the right hand thumb rule (thumb along current, fingers curl in the direction of field lines).
• Magnitude for a long straight wire at a distance r from the wire:

B = (μ₀ I) / (2π r)

where μ₀ = 4π × 10⁻⁷ T·m/A, I is current, r is radial distance. This shows B ∝ I and B ∝ 1/r.

Field due to a circular current loop:

• Field lines pass through the center and form closed loops; at the center of a single circular loop of radius R carrying current I:

B = (μ₀ I) / (2R)

Field due to a solenoid (tightly wound coil):

• Inside a long solenoid the field is approximately uniform and parallel to the axis; outside it is weak and spreads out.
• For an ideal long solenoid with n turns per unit length (n = N/L):

B = μ₀ n I

Direction given by the right hand grip rule: curl fingers in the direction of current in the coils; the thumb points toward the north pole (axis direction) of the solenoid.

Practical notes and observations:

• Small magnetic compasses indicate field direction and are used to map field lines experimentally.
• Magnetic field lines show similarity between permanent magnets and fields produced by currents (Ampère-Maxwell relationship).
• In many devices (motors, loudspeakers, relays) interaction between magnetic fields and currents produces motion or force.

Introduction
When an electric current flows through a straight conductor (wire), it produces a magnetic field in the space around the conductor. This was first observed by Oersted: a compass needle gets deflected when placed near a current-carrying wire, showing that electric currents produce magnetic effects.

Shape and Direction of the Field
The magnetic field lines around a long straight conductor are concentric circles centered on the wire. The direction of the field is given by the right-hand thumb rule: if you hold the wire with your right hand so that the thumb points in the direction of conventional current (from + to −), then the curled fingers show the direction of the magnetic field lines around the wire.

Magnitude of the Field (using Ampere's law)
For a long straight conductor carrying a steady current I, at a distance r from the wire (in air or vacuum), the magnetic field magnitude B is given by Ampere's circuital law. Taking a circular Amperian loop of radius r around the wire:

∮ B·dl = μ0 I_enclosed

Because B is constant on the circular path and tangent to it, B(2πr) = μ0 I, so

B = μ0 I / (2π r)

Here μ0 is the permeability of free space: μ0 = 4π × 10⁻⁷ T·m/A. This formula assumes a sufficiently long (ideally infinite) straight wire and steady current. The field decreases inversely with distance (B ∝ 1/r) and increases linearly with current (B ∝ I).

Units and typical values
Magnetic field B is measured in tesla (T). In common situations around household wires the field is very small (microtesla to millitesla), but near high-current transmission lines the fields can be larger.

Experimental evidence
Common experiments: placing a compass near a straight wire shows the needle tangential to concentric circles; placing iron filings on a sheet above the wire shows circular patterns when current flows; moving the compass closer increases deflection (stronger field), and reversing current reverses the direction of deflection.

Assumptions & limitations
The B = μ0 I/(2πr) formula is for a long straight conductor in a homogeneous medium (air/vacuum). For short wires, nearby magnetic materials, or inside conductors, the field distribution differs.

Summary
A straight current-carrying conductor produces circular magnetic field lines around it. Direction is given by the right-hand thumb rule and magnitude by B = μ0 I/(2π r), falling off as 1/r with distance from the wire.

What is it? A circular loop carrying a steady current I produces a magnetic field in the space around it. The pattern of field lines is similar to that of a bar magnet: lines emerge from one face of the loop, pass through the centre, and return around the outside.

Field shape and direction

• Near the wire of the loop the magnetic field is concentric and circular around each small element of the wire (as given by the right-hand rule for a straight conductor).
• Overall, through the axis of the loop (the line perpendicular to the plane of the loop through its centre) the field is strongest at the centre and decreases as we move away along the axis.
• Direction (Right-hand rule for a loop): Curl the fingers of your right hand in the direction of current flow around the loop. Your thumb points in the direction of the magnetic field on the axis (the 'north' direction of the loop).

Key influences on the field

• Field strength at the centre increases linearly with current I.
• Field strength at the centre decreases with increasing loop radius R (for the same current).
• For N closely wound turns (a coil), the fields from each turn add, increasing the net field approximately by a factor of N.

How the formula is obtained (brief)

The quantitative expression for the magnetic field is obtained using the Biot–Savart law (integration over the circular current). For class 10 purposes you need the result and understanding of dependence on I, R and N rather than the full calculus derivation.

Important special cases

• At the centre of a single circular loop of radius R: B = μ0 I / (2R) directed along the axis.
• At the centre of a coil of N closely wound turns: B = μ0 N I / (2R).
• At a point on the axis a distance x from the centre: B = (μ0 I R^2) / (2 (R^2 + x^2)^(3/2)). This reduces to the centre result when x = 0.

Summary — A current in a circular loop produces a magnetic field like that of a small bar magnet: strongest at the centre, direction given by the right-hand rule, proportional to current and number of turns and inversely related to loop radius.

What is a solenoid? A solenoid is a coil of many turns of insulated wire wound closely in the form of a helix (usually cylindrical). When an electric current flows through the coil, it produces a magnetic field similar to that of a bar magnet: one end acts like a north pole and the other like a south pole.

Shape and direction of the magnetic field

• Inside a long, closely wound solenoid the magnetic field is nearly uniform, strong, and parallel to the axis of the cylinder.
• Outside the solenoid the field is weak and its lines spread out and return from one end of the solenoid to the other, resembling the field of a bar magnet.
• Direction rule (Right-hand rule for solenoid): If the fingers of the right hand curl in the direction of current in the coils, the extended thumb points in the direction of the magnetic field inside the solenoid (toward the solenoid's north pole).

Factors affecting the magnetic field

• Current (I): The field strength is directly proportional to the current through the coils.
• Number of turns per unit length (n = N/L): More turns per metre produce a stronger field.
• Core material: Placing a soft iron core inside the solenoid greatly increases the magnetic field because the core has high magnetic permeability (μ).
• Geometry: For an ideal (very long) solenoid the field inside is nearly uniform; for short solenoids the field is less uniform and weaker at the centre.

Qualitative description of field lines: Draw lines that are straight and parallel inside the solenoid, closely spaced (indicating strong field). Outside, draw wider-spaced curved lines that loop from one end to the other, meeting the pattern of a bar magnet.

Applications (brief): Solenoids are used as electromagnets (lifting ferrous scrap), in electric bells and door locks (as actuators), in relays and solenoid valves, in loudspeaker drivers and many electromechanical devices.

Definition: An electromagnet is a temporary magnet created by passing electric current through a coil of wire (a solenoid). When a soft iron core is placed inside the coil, the magnetic field produced by the coil magnetises the core and the assembly behaves as a strong magnet while current flows.

Construction and working: A simple electromagnet consists of a long coil (solenoid) of insulated copper wire wound on a soft iron core. When current I flows through the coil, each turn produces a magnetic field; the fields add up to produce a strong, nearly uniform field inside the solenoid. The soft iron core concentrates and strengthens the field by becoming magnetised. When the current is switched off, the core loses most of its magnetism and the magnetism disappears (hence it is temporary).

Key properties:

• The magnetic field (and hence strength) of an electromagnet can be controlled by changing the current through the coil or the number of turns of the coil.
• Using a soft iron core greatly increases the magnetic field because the iron has high magnetic permeability and is easily magnetised; soft iron also has small residual magnetism so the magnet turns off quickly.
• The field inside a long solenoid is approximately uniform and strongest near the centre; outside, the field is much weaker.

Factors affecting strength: strength ∝ (number of turns N) × (current I) × (core permeability μ). Strength is inversely related to the length of the coil (for fixed N, a longer coil gives weaker field per unit length).

Comparison with permanent magnets: Electromagnets can be switched on/off and their strength varied; permanent magnets provide a fixed field. Electromagnets are preferred where controllable magnetism or high strength is needed.

Safety and practical notes: High currents produce strong fields but also heat the coil (I²R losses), so insulation, cooling and current limits are important. For very strong electromagnets (e.g., MRI), special designs and materials (and often superconducting coils) are used.

Introduction
When a current-carrying conductor is placed in a magnetic field, it experiences a mechanical force. This phenomenon is called the motor effect and is the basic principle behind electric motors.

Qualitative explanation
A current in a conductor produces a magnetic field around the conductor. When this conductor is placed in an external magnetic field, the two magnetic fields interact. The interaction produces a force on the conductor. The force is maximum when the conductor is perpendicular to the magnetic field lines and zero when it is parallel.

Direction of the force: Fleming's left-hand rule
To find the direction of the force, use Fleming's left-hand rule:

• Hold the left hand so that the thumb, forefinger and middle finger are mutually perpendicular (at right angles).
• Forefinger = direction of magnetic field (from N to S).
• Middle finger = direction of current (from + to − conventional current).
• Thumb = direction of the force (motion) on the conductor.

Quantitative relation
The magnitude of the force (for a straight conductor of length l carrying current I placed in a uniform magnetic field B) is given by:
F = B I l sin θ
where θ is the angle between the conductor (direction of current) and the magnetic field. For the common case when the conductor is perpendicular to the field (θ = 90°):
F = B I l

Vector form
In vector notation, the force on a conductor of length vector L carrying current I in magnetic field B is:
F = I (L × B)

Torque on a rectangular coil (basic motor)
A rectangular coil carrying current in a uniform magnetic field feels forces on its two sides; these forces form a couple producing a torque that tends to rotate the coil. For a coil with N turns and area A carrying current I in a uniform field B, the maximum torque is approximately:
τ = N I A B (for the coil when its plane is parallel to B and the torque is maximum)

How this gives rotation in a motor
In a simple DC motor a rectangular coil is placed in a magnetic field. Current through the coil produces forces on the sides causing rotation. A commutator (split-ring) reverses the current every half turn so that the torque keeps acting in the same rotational sense, producing continuous rotation.

Important points to remember

• Force is proportional to current I, magnetic field B and length l (when perpendicular).
• Force is zero when conductor is parallel to field (θ = 0° or 180°), maximum at θ = 90°.
• Direction found by Fleming's left-hand rule (thumb = force, forefinger = field, middle finger = current).

What it is: A simple electric motor converts electrical energy into mechanical energy using the magnetic effect of current. It consists of a current‑carrying coil placed in a magnetic field; interaction between the coil's magnetic field and the external field produces a torque that turns the coil.

Main parts:

• Rectangular coil (armature) of insulated wire (often with many turns)
• Permanent magnet or electromagnet providing a stationary magnetic field (north and south poles)
• Split‑ring commutator (a pair of half‑rings) that reverses the current in the coil every half turn
• Carbon or metal brushes that make sliding electrical contact with the commutator
• Soft iron core inside the coil (optional) to increase magnetic flux and torque

How it works (stepwise):

1. When a current flows through the coil, each side of the rectangular coil carries current in opposite directions.
2. Each side experiences a magnetic force: F = B I L (where B is magnetic field, I current, L length of the side in the field). One side gets a force upward, the opposite side gets a force downward.
3. These two equal and opposite forces form a couple (torque) that tends to rotate the coil about its axis.
4. After the coil rotates through 90°, if the current direction remained the same the torque would reverse direction and stop the rotation. The split‑ring commutator reverses the current in the coil every half‑turn so that the direction of forces stays the same relative to the coil, producing continuous rotation.
5. Fleming’s left‑hand rule gives the direction of force: First finger = Field (B), Second finger = Current (I), Thumb = Motion (force/ thrust).

Energy conversion: Electrical energy supplied to the coil is converted into mechanical work done in rotating the coil against loads and to overcome friction.

Factors affecting torque and performance:

• Magnetic field strength (B) — stronger magnets give larger torque.
• Current (I) through the coil — torque is proportional to I.
• Number of turns (N) and area (A) of the coil — more turns and larger area increase torque (torque ∝ NIA).
• Presence of soft iron core concentrates flux and increases torque.
• Load and friction — higher load reduces steady speed.

Important practical notes: The commutator and brushes cause sparking and wear; in larger motors, more complex commutation (brushless designs) or electronic controllers are used. DC motors follow the same basic principle as the simple motor described.

Definition: Electromagnetic induction is the phenomenon in which an electromotive force (emf) is induced in a conductor when the magnetic flux linked with it changes with time.

Discovery and basic idea: Michael Faraday discovered that a changing magnetic field near a closed loop produces an emf and hence a current if the loop is closed. A simple demonstration is moving a bar magnet toward and away from a coil: a current appears in the coil whenever the magnetic flux through the coil changes.

Magnetic flux: Magnetic flux (Φ) through an area A in a magnetic field B is Φ = B A cosθ, where θ is the angle between the field and the area normal. Flux measures the amount of magnetic field passing through the surface.

Faraday's law: The induced emf in a coil is equal to the negative rate of change of magnetic flux through the coil. For a coil of N turns, ε = -N (dΦ/dt). The negative sign is explained by Lenz's law and indicates the direction of the induced emf.

Lenz's law: The induced current flows in such a direction that its magnetic field opposes the change in the magnetic flux that produced it. Lenz's law is a statement of conservation of energy and gives the sign (direction) of the induced emf.

Ways to change flux: Flux through a loop can be changed by (a) changing the magnetic field strength B, (b) changing the area A of the loop within the field, or (c) changing the angle θ between the field and the loop. Relative motion between magnet and coil also changes flux.

Simple formulas for special cases: For a straight conductor of length l moving with velocity v perpendicular to a magnetic field B, the motional emf induced between its ends is ε = B l v. For a coil with N turns, total emf scales by N.

Eddy currents: Changing magnetic flux in bulky conductors induces circulating currents called eddy currents. These produce heating and oppose the flux change; they are reduced in devices by using laminated cores.

Energy and practical note: Work is required to oppose the magnetic reaction when trying to change the flux. That mechanical work is converted into electrical energy (generator) or electrical energy is converted to mechanical work (motor).

Basic idea: When the magnetic flux through a closed circuit changes, an emf (and hence a current, if the circuit is closed) is induced. The direction of the induced current is such that it opposes the change of flux that produced it. This statement is called Lenz's law and is a consequence of conservation of energy.

Faraday–Lenz relationship (qualitative form): The induced emf tries to oppose the change in magnetic flux. In mathematical form (Faraday's law with Lenz's sign):

emf = -N (dΦ/dt)

Here N is the number of turns and Φ is the magnetic flux through one turn. The minus sign encodes Lenz's law (the induced emf has polarity that opposes the change).

Steps to determine direction of induced current:

1. Decide how the magnetic flux through the loop is changing (increasing or decreasing) and its direction (into or out of the plane).
2. By Lenz's law, the induced magnetic field produced by the induced current will oppose that change. If external flux is increasing into the page, the induced field will be out of the page; if the external flux is decreasing into page, the induced field will be into the page.
3. Use the right-hand rule for a current loop (right-hand grip rule): curl your fingers in the direction of current; your thumb shows the direction of the magnetic field produced by that current. Choose the current direction that produces the required induced field from step 2.
4. If dealing with a straight conductor moving in a magnetic field, you can use Fleming's right-hand rule: thumb = motion of conductor, forefinger = magnetic field (from N to S), middle finger = direction of induced current.

Examples of common situations:

• Magnet with north pole approaching a stationary coil: the flux into the coil increases (say into the page). Induced current produces a magnetic field out of the page (to oppose increase). Using right-hand rule, the induced current is anticlockwise (when viewed from the magnet side).
• Magnet receding from coil: the flux into the coil decreases. Induced current produces additional field into the page (to oppose decrease). That gives the opposite current direction (clockwise in the previous view).

Why Lenz's law is important: It ensures energy conservation. If the induced current helped the flux change instead of opposing it, a self-amplifying loop would produce energy from nothing. Lenz's law requires work be done to change flux (e.g., you must push the magnet), and that mechanical work converts to electrical energy (and usually heat) in the circuit.

Relation to observable effects: Lenz's law explains eddy current braking (metal plate in a magnetic field slows down when moving), induction cooktops (eddy currents heat the pan), damping of moving magnetic systems, and operation of generation devices (AC generators produce alternating emf because flux through coil changes periodically).

Basic idea: An electric generator converts mechanical energy into electrical energy using electromagnetic induction. When a conductor (or coil) moves so that the magnetic flux through it changes, an emf is induced in it (Faraday's law). The direction of the induced current is given by Lenz's law and Fleming's right-hand rule for generators.

Principle (Faraday's law): The induced emf in a coil of N turns is emf = -N dΦ/dt, where Φ is the magnetic flux through one turn. If a rectangular coil of area A rotates with angular speed ω in a uniform magnetic field B such that the angle between the field and normal to the coil is θ = ωt, the flux is Φ = B A cos(ωt) and the instantaneous emf becomes e(t) = N B A ω sin(ωt). Thus the generator naturally produces alternating emf.

Construction & working (simple AC generator / alternator): A coil (armature) is placed between poles of a magnet. The coil is rotated by a prime mover (steam turbine, water turbine, engine, wind turbine). Slip rings are attached to the rotating coil and stationary brushes contact the rings to take alternating output to the external circuit. As the coil rotates, the magnetic flux through the coil changes sinusoidally and an alternating emf is induced. The frequency of the generated emf is related to the rotation speed.

DC generator (dynamo): In a DC generator the rotating coil produces an alternating emf internally, but a split-ring commutator (instead of slip rings) reverses the connection of the coil to the external circuit every half rotation. This converts the alternating emf into a unidirectional (pulsating) current in the external circuit (more steady DC is obtained using multiple coils and smoothing circuits).

Important parts: field magnets (or electromagnets), armature (rotating coil), brushes, slip rings (for AC) or commutator (for DC), and a prime mover to supply mechanical rotation.

Direction of induced current: Use Fleming's right-hand rule: thumb — motion of conductor, first finger — magnetic field (N to S), second finger — induced current (conventional).

Practical considerations: Alternators are used for large-scale power generation because AC is easy to transform and transmit. DC generators are used where DC is required or where commutation and smoothing produce nearly steady DC (e.g., some battery charging, small motors). Modern car charging systems use alternators plus rectifiers (diodes) to supply DC to charge the battery.

Applications summary: power stations (thermal, hydro, nuclear) use large alternators to supply mains electricity; wind turbines use large generators to convert wind energy; small portable petrol/diesel generators supply backup or remote power; bicycle dynamos power lights; hand-crank torches and emergency generators are small-scale examples.

Overview: When an electric current flows through a conductor it produces a magnetic field around it. This magnetic effect is used in many devices and practical applications. The essential idea is: an electromagnet or magnetic field, produced by a current, can exert forces or torques on magnetic materials or current-carrying conductors and so can be used for switching, sensing, motion and transduction (electrical → mechanical → sound etc.).

Key devices and how they work

• Electromagnet: A coil of insulated wire carrying current becomes magnetic; placing a soft-iron core inside greatly increases the field (core becomes magnetised). Used in cranes to lift scrap, relays, magnetic locks.
• Solenoid (electromagnetic actuator): A long coil that produces an almost uniform magnetic field inside. The magnetic field can pull a ferromagnetic plunger to make mechanical motion (used in valves, starters, door-lock actuators).
• Electric bell / buzzer: Current through a coil produces a magnetic field that attracts an armature. The armature movement interrupts the circuit (or uses spring return) causing repeated make/break and a ringing/buzzing action.
• Relay & Electromagnetic switch: A small current energises a coil to produce a magnetic field that closes (or opens) contacts to switch a larger current — used in control circuits, automotive electronics.
• Moving-coil galvanometer: A coil suspended in a magnetic field experiences a torque proportional to current; its angular deflection (measured by a pointer) indicates very small currents. By adding a shunt it becomes an ammeter; by adding a series resistor it becomes a voltmeter.
• Electric motor (DC motor): A current-carrying loop/armature placed in a magnetic field experiences forces on opposite sides of the loop, producing a torque that rotates the shaft. A commutator reverses current direction in the coil every half-turn to maintain continuous rotation.
• Loudspeaker / Headphone: An audio-frequency current in a voice coil placed in a permanent magnetic field produces oscillatory forces on the coil; the coil drives a cone or diaphragm to produce sound waves.
• Magnetic recording & playback, telephone receivers: Use magnetic fields generated by currents (and vice versa) to record or reproduce signals.
• Magnetic resonance imaging (MRI) — applied example: Extremely strong magnetic fields (from large superconducting coils) and radio-frequency currents are used in medical imaging — an advanced application of magnetic effects of current.

Principles to remember

• Current produces magnetic field; the field exerts force on other currents and on magnetic materials.
• A coil with many turns multiplies the magnetic effect (field ∝ number of turns × current).
• Force on a current-carrying conductor in a magnetic field is used to produce motion (motors) and sound (speakers).
• Magnetic devices can be used as switches (relays), indicators (galvanometers), transducers (speakers, microphones), actuators (solenoids), and in heavy lifting (electromagnetic cranes).

Safety/notes: Electromagnets and coils heat when current flows; insulation and rated currents must be observed. Strong magnetic fields can affect sensitive electronics and magnetic storage media.