Text book: International A/AS Level p314-327, 335-346
Key Words: Magnetic force, Magnetic flux density, Tesla, Fleming’s left-hand rule, Top balance, Current balance, Hall probe, Electric Motor
7.1 Force on a current carrying conductor in a magnetic field and Fleming’s left-hand rule
Definition of Magnetic flux density B
Magnetic flux density is the force per unit current per unit length acting on a conductor placed at 90° to the field. unit: tesla (T)
F=force on the conductor, in N
B =magnetic flux density, in T
I=current in the conductor, in A l =length of the conductor in the field, in m = angle between the conductor and the magnetic field
(a): the current and field are parallel,
The magnetic field from the current is affected by the magnetic field from the magnet; this produces a force.
Fleming’s left-hand rule First finger points in the direction of the magnetic field (North to South).Second finger points in the direction of conventional current (positive to negative).Thumb points in the direction of the force on the conductor.
7.2 Force on a changed particle in a magnetic field (1)Centripetal force of circular motion is provided by magnetic force:
F= force on a charged particle, in N
B = magnetic flux density, in T q = charge of particle, in C v= speed of the particle, in = angle between the direction of moving particle and the magnetic field
(a), F = 0;
When charged particle move into a uniform magnetic field perpendicularly, the track is curve
(see right fig.)
For the negative charge the second finger points opposite direction of velocity
(2)Why for changed particle?
Consider a conductor of length l having n free electrons per unit volume. A current, I, is flowing through it.
In this piece of conductor there are free electrons. Suppose that all these free electrons pass through the end x, in time, t. This means that the current is given by
where q represents the charge of one electron. If there is a magnetic field, B, at to the current, the conductor will experience a force of magnitude
Now, this is the sum of the forces acting on N free electrons as they move through the piece of conductor.
Therefore, force per electron, f , is given by
7.3 Force between very long current carrying conductors
Parallel wires with current flowing in the same direction, attract each other.
Parallel wires with current flowing in the opposite direction, repel each other.
Conductor A (very long wire) produces a magnetic field which perpendicular to the current flow in conductor B (very long wire).
The force acting on B will be at right angles to the current flow and at right angles to the magnetic field produced by A:
A similar argument will show that the force acting on A will be at right angles to the current flow and at right angles to the magnetic field produced by B:
Hence the forces and are equal and in opposite direction (in other words, the conductors A and B are attracted to each other):
*Definition of Ampere: When two long straight parallel conductors of negligible area of cross-section are placed one meter apart in a vacuum, if the current in each conductor is one ampere, then the force per meter on each conductor is 2 x 10-7 N.
The force acting on unit of length of conductor is ** when and = 1 A and r = 1 m