Magnetic fields due to currents
Section: Magnetic Fields | Syllabus: Cambridge A Level Physics (9702)
Field Patterns around Conductors
Using the Right-Hand Grip Rule: Grip the conductor with your right hand, thumb pointing in the direction of conventional current. Your fingers curl in the direction of the magnetic field.
1. Long Straight Wire
Field lines are concentric circles centered on the wire. Separation increases with distance (field gets weaker: B ∝ 1/r).
2. Flat Circular Coil
Field lines are circular near the wire but become straighter near the center. At the very center, the field is perpendicular to the plane of the coil.
Determining Poles (Clock Rule)Looking at the face of a coil/solenoid:
- Anticlockwise Current: Arguments N pole.
- Clockwise Current: Arguments S pole.
3. Long Solenoid
Inside the solenoid, field lines are parallel and equally spaced, indicating a uniform magnetic field. Outside, the pattern resembles a bar magnet.
Solenoids vs Bar MagnetsA solenoid acts like a magnet with N and S poles. The field strength can be increased by:
- Increasing the current (I).
- Increasing the number of turns per unit length (n).
- Inserting a ferrous (soft iron) core. This concentrates the magnetic flux, practically increasing the field strength (permeability μ > _0).
Applications: Electromagnets are used in MRI scanners, particle accelerators, speakers, and magnetic levitation (Maglev) trains.
Forces between Currents
Current-carrying conductors exert magnetic forces on each other.
- Parallel, same direction: Attract.
- Parallel, opposite direction: Repel.
Wire A produces a magnetic field at the position of Wire B. Wire B, carrying a current in this field, experiences a force (refer to Fleming's Left Hand Rule). By Newton's 3rd Law, Wire A experiences an equal and opposite force.
Common Sketching ErrorWhen drawing the combined field of two wires, ensure field lines do not cross. For attracting wires, lines encircle both (like a rubber band pulling them together). For repelling wires, lines compress between them.
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