Physics Learning Guide
Magnetic Effects of Electric Current
Whenever electric current flows through a conductor, it produces a magnetic field around the conductor. This connection between electricity and magnetism explains how electromagnets, electric motors, loudspeakers, generators and many other devices work.
What Does “Magnetic Effect of Current” Mean?
The magnetic effect of electric current is the production of a magnetic field by moving electric charges or by current flowing through a conductor.
This effect was demonstrated by Hans Christian Oersted, who observed that a current-carrying wire could deflect a nearby compass needle. This showed that electric current and magnetism are closely related.
Magnetic Field
A magnetic field is the region around a magnet, a current-carrying conductor or a moving charge where a magnetic force can be experienced.
The magnetic field is represented by the symbol B. Its SI unit is the tesla (T).
Magnetic Field Lines
Magnetic field lines are imaginary lines used to show the direction and relative strength of a magnetic field.
- Outside a bar magnet, field lines emerge from the north pole and enter the south pole.
- Inside the magnet, they continue from the south pole to the north pole, forming closed curves.
- The direction of the magnetic field at any point is along the tangent to the field line at that point.
- Closer field lines represent a stronger magnetic field.
- Magnetic field lines never intersect one another. If they did, the field would have two directions at the same point.
Magnetic Field Around a Straight Current-Carrying Wire
A straight wire carrying current produces circular magnetic field lines around it. The wire passes through the centre of these circles.
Right-Hand Thumb Rule
Hold a straight conductor in your right hand with your thumb pointing in the direction of conventional current. The curled fingers show the direction of the magnetic field around the conductor.
Magnetic Field Due to a Long Straight Wire
B = μ0I / 2πr
- B = magnetic field, measured in tesla (T)
- μ0 = permeability of free space, equal to 4π × 10−7 T·m/A
- I = current in the wire, measured in amperes (A)
- r = perpendicular distance from the wire, measured in metres (m)
This formula is used for a long, straight conductor when the magnetic field is required at a distance r from the wire.
The field becomes stronger when the current increases and weaker when the distance from the wire increases.
Numerical Example: Field Near a Straight Wire
Given:
- Current, I = 5 A
- Distance from the wire, r = 0.10 m
- μ0 = 4π × 10−7 T·m/A
Formula:
B = μ0I / 2πr
Substitution:
B = [(4π × 10−7) × 5] / [2π × 0.10]
B = 1.0 × 10−5 T
Final answer: The magnetic field is 1.0 × 10−5 T.
Magnetic Field of a Circular Current-Carrying Coil
When a wire is bent into a circular loop and current flows through it, the magnetic fields produced by different parts of the loop combine near its centre. The field at the centre is directed along the axis of the loop.
Field at the Centre of a Circular Coil
B = μ0I / 2R
For a coil with N closely wound turns:
B = μ0NI / 2R
- B = magnetic field at the centre, in tesla (T)
- μ0 = permeability of free space, in T·m/A
- I = current, in amperes (A)
- R = radius of the coil, in metres (m)
- N = number of turns, a dimensionless quantity
The formula is used to calculate the magnetic field at the centre of a circular coil. Increasing the current or the number of turns increases the field, while increasing the radius decreases the field.
Direction of the Field of a Coil
Curl the fingers of your right hand in the direction of current in the coil. Your thumb points towards the magnetic north side of the coil.
Solenoid and Electromagnet
A solenoid is a long cylindrical coil made by winding insulated wire into many closely spaced turns. When current flows through it, the solenoid produces a magnetic field similar to the field of a bar magnet.
The field inside a long solenoid is approximately uniform, especially near its central region. A soft iron core can be placed inside the solenoid to make a strong electromagnet.
Magnetic Field Inside a Long Solenoid
B = μ0nI
- B = magnetic field inside the solenoid, in tesla (T)
- μ0 = permeability of free space, in T·m/A
- n = number of turns per unit length, in turns per metre (m−1)
- I = current, in amperes (A)
This ideal formula is used for a long solenoid, away from its ends. The magnetic field becomes stronger when the number of turns per unit length or the current increases.
Uses of Electromagnets
- Electric bells
- Relays and circuit breakers
- Electromagnetic cranes
- Speakers and headphones
- Some medical and industrial equipment
Why Soft Iron Is Used
Soft iron becomes strongly magnetised when current flows through the coil and loses most of its magnetism when the current is switched off. This makes it useful when a magnet must be controlled electrically.
Force on a Current-Carrying Conductor in a Magnetic Field
A current-carrying conductor placed in an external magnetic field may experience a force. This happens because the magnetic field produced by the current interacts with the external magnetic field.
Force on a Straight Current-Carrying Conductor
F = BIL sin θ
- F = magnetic force, in newtons (N)
- B = magnetic field strength, in tesla (T)
- I = current, in amperes (A)
- L = length of conductor in the magnetic field, in metres (m)
- θ = angle between the direction of current and the magnetic field
This formula is used when a straight conductor of length L carries current in a magnetic field. The force is greatest when the conductor is perpendicular to the field, because sin 90° = 1. The force is zero when the conductor is parallel to the field, because sin 0° = 0.
Fleming’s Left-Hand Rule
Stretch the thumb, first finger and second finger of your left hand so that they are mutually perpendicular:
- First finger points in the direction of the magnetic field.
- Second finger points in the direction of current.
- Thumb points in the direction of force or motion.
Numerical Example: Force on a Wire
Given:
- B = 0.20 T
- I = 3 A
- L = 0.50 m
- The wire is perpendicular to the field, so θ = 90°
Formula:
F = BIL sin θ
Substitution:
F = 0.20 × 3 × 0.50 × sin 90°
F = 0.20 × 3 × 0.50 × 1
Final answer: F = 0.30 N.
Electric Motor: Converting Electrical Energy into Mechanical Energy
An electric motor is a device that converts electrical energy into mechanical energy. It works on the principle that a current-carrying coil placed in a magnetic field experiences a force.
Main Parts of a Simple Motor
- Coil: A rectangular coil that carries current.
- Magnet: Provides the magnetic field.
- Split-ring commutator: Reverses the current in the coil after every half-turn.
- Carbon brushes: Maintain contact with the rotating commutator.
- Axle: Allows the coil to rotate and transfer motion.
The forces on the two opposite sides of the coil act in opposite directions. These forces produce a turning effect, causing the coil to rotate. The commutator reverses the current at the correct time so that the rotation continues in the same direction.
Torque on a Current-Carrying Coil
The turning effect of a force is called torque. A current-carrying coil in a magnetic field can experience torque.
Torque on a Coil
τ = NIAB sin θ
- τ = torque, in newton-metres (N·m)
- N = number of turns in the coil
- I = current, in amperes (A)
- A = area of the coil, in square metres (m2)
- B = magnetic field strength, in tesla (T)
- θ = angle between the magnetic field and the normal to the plane of the coil
This relationship is useful for understanding the turning effect in electric motors and moving-coil instruments. The torque is largest when sin θ has its maximum value of 1.
Electromagnetic Induction
Electromagnetic induction is the production of an induced emf or induced current when the magnetic flux linked with a conductor or coil changes.
A changing magnetic field can be produced by moving a magnet towards or away from a coil, moving the coil in a magnetic field, or changing the current in a nearby coil.
Magnetic Flux
Magnetic flux is a measure of the magnetic field passing through a surface.
Φ = BA cos θ
- Φ = magnetic flux, measured in weber (Wb)
- B = magnetic field, measured in tesla (T)
- A = area of the surface, measured in square metres (m2)
- θ = angle between the magnetic field and the normal to the surface
This formula is used when the magnetic field is uniform over the surface.
Faraday’s Law of Electromagnetic Induction
ε = −N ΔΦ / Δt
- ε = induced emf, measured in volts (V)
- N = number of turns in the coil
- ΔΦ = change in magnetic flux, measured in webers (Wb)
- Δt = time interval, measured in seconds (s)
The formula is used to calculate the average induced emf when the magnetic flux changes during a known time interval. The negative sign represents Lenz’s law: the induced effect opposes the change that produces it.
Lenz’s Law in Simple Words
The induced current flows in such a direction that its magnetic effect opposes the change in magnetic flux. This is why pushing a magnet into a coil and pulling it out produce induced currents in opposite directions.
Electric Generator
An electric generator converts mechanical energy into electrical energy. It works on electromagnetic induction.
When a coil rotates in a magnetic field, the magnetic flux linked with the coil changes. An induced emf is therefore produced. In an alternating-current generator, the direction of the induced current changes periodically. A slip-ring arrangement is used to collect the alternating current.
An electric motor and a generator are closely related but perform opposite energy conversions:
| Device | Energy conversion | Main principle |
|---|---|---|
| Electric motor | Electrical energy → Mechanical energy | Force on a current-carrying coil in a magnetic field |
| Electric generator | Mechanical energy → Electrical energy | Electromagnetic induction |
Important Relationships to Remember
| Situation | Relationship | What happens when a quantity increases? |
|---|---|---|
| Long straight wire | B = μ0I / 2πr | Field increases with current and decreases with distance. |
| Circular coil | B = μ0NI / 2R | Field increases with turns and current. |
| Long solenoid | B = μ0nI | Field increases with turns per unit length and current. |
| Wire in an external field | F = BIL sin θ | Force is greatest when the wire is perpendicular to the field. |
| Induction | ε = −N ΔΦ / Δt | Faster or greater flux change produces greater induced emf. |
Common Mistakes and Misconceptions
- Confusing current direction: Conventional current is taken to flow from positive to negative outside a source. Electron flow in a metal is in the opposite direction.
- Mixing up the right-hand and left-hand rules: The right-hand thumb rule gives the direction of the magnetic field around a current-carrying wire. Fleming’s left-hand rule gives the direction of force on a current-carrying conductor.
- Forgetting the angle in F = BIL sin θ: The angle is between the current direction and the magnetic field.
- Assuming every conductor experiences maximum force: The force is maximum only when the conductor is perpendicular to the magnetic field.
- Confusing motor and generator: A motor uses electrical energy to produce motion, whereas a generator uses motion to produce electrical energy.
- Thinking a magnetic field must always produce current: Current is induced only when the magnetic flux linked with a circuit changes.
- Ignoring units: Magnetic field is measured in tesla, force in newtons, flux in webers and emf in volts.
Practical Applications
Electric Bells
An electromagnet attracts an iron armature when current flows. The contact then breaks and reforms repeatedly, producing the ringing action.
Speakers
A current-carrying coil interacts with a permanent magnetic field and moves a diaphragm. The diaphragm creates sound waves.
Scrap-Metal Cranes
Large electromagnets can lift iron and steel objects when switched on and release them when switched off.
Power Generation
Generators use electromagnetic induction to convert mechanical rotation into electrical energy.
Important Points for Students
- A current-carrying conductor produces a magnetic field.
- The magnetic field around a straight wire consists of circular field lines.
- The right-hand thumb rule gives the direction of the magnetic field around a straight current-carrying wire.
- A coil with many turns produces a stronger magnetic field than a single loop carrying the same current.
- A solenoid behaves like a bar magnet and can be used to make an electromagnet.
- A current-carrying conductor in an external magnetic field can experience a force.
- Fleming’s left-hand rule gives the direction of this force.
- Electric motors are based on the force on a current-carrying coil.
- Electromagnetic induction is the production of emf due to changing magnetic flux.
- Generators are based on electromagnetic induction.
Quick Recap
- Electric current produces a magnetic field.
- For a long straight wire, B = μ0I / 2πr.
- For a circular coil, the field at the centre is B = μ0NI / 2R.
- Inside a long solenoid, the ideal field is B = μ0nI.
- A current-carrying conductor in a magnetic field experiences force: F = BIL sin θ.
- An electric motor converts electrical energy into mechanical energy.
- Changing magnetic flux produces induced emf according to ε = −N ΔΦ / Δt.
- An electric generator converts mechanical energy into electrical energy.