Magnetic Fields
Understand magnetic field lines, magnetic flux, the force on current-carrying conductors, and how electric motors work.
Magnetic Field Lines
A magnetic field is a region of space where a magnetic force is exerted on moving charges or magnetic materials. We represent magnetic fields using field lines that show the direction and relative strength of the field.
Bar Magnet Field Pattern
Field lines travel from North to South outside the magnet
Key Rules
- • Lines go from N to S outside the magnet
- • Lines never cross each other
- • Closer lines = stronger field
- • Lines form closed loops
Magnetic Flux (Φ)
Φ = BA cosθ
where B = magnetic flux density (T), A = area (m²), θ = angle between B and the area normal. Unit: Weber (Wb)
Key concept: Magnetic flux density B (measured in Tesla, T) describes the strength of the field at a point. 1 T = 1 Wb/m².
Force on a Current-Carrying Conductor
When a wire carrying current is placed in a magnetic field, it experiences a force. This is the principle behind electric motors, loudspeakers, and many other devices.
The Motor Effect: F = BIL sinθ
F
Force (N)
B
Flux density (T)
I
Current (A)
L
Length (m)
The Right-Hand Rule
To find the direction of the force on a current-carrying conductor:
- 1. Point your fingers in the direction of the current (I)
- 2. Curl them in the direction of the magnetic field (B)
- 3. Your thumb points in the direction of the force (F)
Note: The force is maximum when the wire is perpendicular to the field (θ = 90 degrees) and zero when parallel (θ = 0 degrees).
The DC Electric Motor
A DC motor converts electrical energy into rotational kinetic energy using the motor effect. A current-carrying coil placed in a magnetic field experiences forces that cause it to rotate.
Key Motor Components
Coil (Armature)
A rectangular loop of wire that rotates in the magnetic field when current flows through it.
Permanent Magnets
Provide a uniform magnetic field in which the coil rotates.
Split-Ring Commutator
Reverses the current direction every half-turn so the coil continues rotating in the same direction.
Carbon Brushes
Maintain electrical contact with the spinning commutator to supply current.
Increasing Motor Speed
• Increase the current -- greater force on the conductor
• Use a stronger magnet -- increases B
• Add more turns to the coil -- each turn contributes additional force
• Use a soft iron core -- concentrates the magnetic field through the coil
Key Vocabulary
Magnetic Flux Density (B)
The strength of a magnetic field at a point, measured in Tesla (T). It represents force per unit current per unit length.
Magnetic Flux (Φ)
The total magnetic field passing through a given area, measured in Webers (Wb). Φ = BA cosθ.
Motor Effect
The force experienced by a current-carrying conductor in a magnetic field, given by F = BIL sinθ.
Commutator
A split-ring device in a DC motor that reverses current direction every half-turn to maintain continuous rotation.
Worked Examples
A 0.5 m wire carries 3 A in a uniform field of 0.2 T at 90 degrees. Find the force.
Step 1: Identify: B = 0.2 T, I = 3 A, L = 0.5 m, θ = 90 degrees
Step 2: Apply F = BIL sinθ = 0.2 × 3 × 0.5 × sin 90 degrees
Step 3: F = 0.2 × 3 × 0.5 × 1 = 0.30 N
Calculate the magnetic flux through a 0.04 m² coil in a 1.5 T field, with the coil perpendicular to the field.
Step 1: Identify: B = 1.5 T, A = 0.04 m², θ = 0 degrees (normal to coil is parallel to B)
Step 2: Apply Φ = BA cosθ = 1.5 × 0.04 × cos 0 degrees
Step 3: Φ = 1.5 × 0.04 × 1 = 0.06 Wb
Explain why a split-ring commutator is necessary in a DC motor.
Step 1: Without a commutator, the forces on the coil would reverse every half-turn.
Step 2: The coil would oscillate back and forth instead of rotating continuously.
Step 3: The commutator reverses the current direction every half-turn, ensuring the force always pushes the coil in the same rotational direction, producing continuous spinning.
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Magnetic field lines around a bar magnet travel from:
Question 2
A wire of length 0.8 m carries a current of 5 A perpendicular to a 0.3 T magnetic field. What force acts on the wire?
Question 3
The unit of magnetic flux is the:
Question 4
In a DC motor, the purpose of the split-ring commutator is to:
Question 5
A current-carrying wire is placed parallel to a magnetic field. The force on the wire is:
Key Concepts Summary
- ●Magnetic field lines go from North to South outside the magnet and never cross.
- ●Magnetic flux Φ = BA cosθ, measured in Webers (Wb).
- ●The motor effect force is F = BIL sinθ, maximum when wire is perpendicular to field.
- ●The right-hand rule determines force direction on a current-carrying conductor.
- ●A DC motor uses a split-ring commutator to maintain continuous rotation.