Summary — What This Chapter Covers
- A magnetic field is a field of force produced by moving charges or permanent magnets; lines run N to S.
- F = BIL sin θ, direction by Fleming's left-hand rule; B is defined as force per unit current per unit length (tesla).
- F = BQv sin θ; a charge moving perpendicular to a uniform field moves in a circle; Hall voltage VH = BI/(ntq).
- Velocity selector: crossed E and B fields pass undeflected only particles with v = E/B.
- Φ = BA; flux linkage NΦ; Faraday: e.m.f. = rate of change of flux linkage; Lenz: induced e.m.f. opposes the change.
1. Concept of a Magnetic Field
20.1
A field of force
A magnetic field is a region in which a magnet, a magnetic material, or a moving charge experiences a force. It is produced either by moving charges (currents) or by permanent magnets.
Field lines show the direction a free north pole would move: out of the north pole and into the south pole of a magnet. They never cross; closer lines mean a stronger field. A uniform field has parallel, equally spaced lines. A dot (•) means a field out of the page and a cross (×) into the page.
Practice Question
Two bar magnets are placed end to end with their north poles facing. Describe the field between them.
2. Force on a Current-Carrying Conductor
20.2
F = BIL sin θ
A conductor carrying a current in a magnetic field may experience a force. Its size depends on the flux density B, the current I, the length L in the field and the angle θ between the wire and the field: no force when the wire is parallel to the field, maximum when perpendicular. The direction is given by Fleming’s left-hand rule: First finger = Field, seCond finger = Current (conventional), thuMb = Motion (force).
Magnetic flux density is defined as the force acting per unit current per unit length on a wire placed at right angles to the field. 1 tesla = 1 N A−1 m−1.
Force on a wire
F = BIL sin θ B = F/(IL) when θ = 90°
Worked Example
A wire 0.15 m long carries 3.0 A at 30° to a field of 0.080 T. Find the force on it.
Practice Question
A magnet sits on a top-pan balance with a horizontal wire through its field. 0.050 m of wire is in the field. With 4.0 A flowing, the reading rises by 2.4 g. Find B.
3. Force on a Moving Charge
20.3
F = BQv sin θ
A current is a flow of charges, so each moving charge feels a force F = BQv sin θ. For direction, use Fleming’s left-hand rule with the second finger along the conventional current: for a negative charge, point it opposite to the velocity.
Circular motion. A charge moving perpendicular to a uniform field feels a force of constant size perpendicular to its velocity, so it moves in a circle: BQv = mv2/r, giving r = mv/(BQ). Faster or heavier particles make larger circles.
Hall voltage.
H
H
Hall probe
H
Velocity selection.
Moving charge
F = BQv sin θ r = mv/(BQ) VH = BI/(ntq) v = E/B
Practice Question
25
−3
H
4
−1
4. Magnetic Fields Due to Currents
20.4