Flux and Flux Linkage (Magnetic)
An EMF is generated in any conductor that experiences a changing magnetic flux.
For a conducting coil, the size of the effect increases with increasing turns of the wire, so we refer to a change in flux linkage.
Flux linkage is the is the magnetic flux in respect to a coil. To find the flux linkage, its magnetic flux (B x A, where B is the magnetic flux denisty (field strength), and A is the area) times by the number of coils. Flux Linkage (NΦ) = NBA.
Both Flux and Flux Linkage are measured in Weber (Wb).
The flux density (B) is a measure of the magnetic field strength. It tells us how close together the magnetic field lines are. Flux density is measured in Tesla (T).
1 Tesla = 1 Weber/ 1 m^2. T = WBm^-2.
Faraday's law, Lenz's law
Law of induction. Discovered in the 1830's.
The magnitude of the emf is directly proportional to the rate of change of flux linkage.
E = d(NΦ)/dt
The induced emf must cause the current in the circuit to flow in a direction as to oppose the change in flux linkage that creates it.
E = -d(NΦ)/dt.
Faraday's Law implies that the energy is being created from nothing. Lenz's law is just an example of the law of conservation of energy.
Flemings Right Hand rule.
First finger : Field (magnetic field)
Second finger: Current (induced current)
Thumb : Motion (of the conductor)
The right hand rule is used when we are generating electricity.
Lines of Magnetic Flux
-Arrows indicate that the forces act on a magnetic north pole
- the lines are continuous, and never cross.
- the closer the lines, the stronger the magnetic field.
A wire carrying a current has a circular magnetic field around it.
Magnetic fields combine, and cancel out.
We can use the right hand grip rule to find out the magnetic field around a current carrying wire. The thumb is the direction of conventional current, and your fingers are the direction of the magnetic field around the wire.
A length of wire, L, carrying a current, I, in a magnetic field strength of B, experiences a magnetic force, F, as long as there is a component of the field at right angles to the current.
The maximum force will be when the current is at right angles to the direction of the field.
F = BILSin(θ).
The length of wire is the length of wire within the magnetic field, not the length of the wire in general. θ is the angle that the wire is to the magnetic field lines.
So basically this equation tells us how much force acts on a wire carrying a current in a magnetic field. If θ is 0, then there is no force, as Sin(0) = 0.
Fleming's Left Hand rule
We can find the direction of this force by using Fleming's left-hand rule.
First finger - Field (magnetic field)
SeCond finger - Current (direction of conventional current)
Thumb - Thrust (direction of the force).
To distinguish between using the left hand rule and the right hand rule might seem tricky at first, but its quite simple.
You use the left hand rule to work out the direction of the force on a wire in a magnetic field.
You use the right hand rule to find the direction of the induced current.
Charged Particle Beams
A charge, Q, moving with a velocity, v, moving through a magnetic field, B, also experiences a magnetic force, F. Once again there has to be a component of the field acting perpendicular to the direction of charge movement.
The maximum force will be when θ is 90.
You can find the direction of the force using Fleming's left-hand rule.
The movement is often usually circular, so we can combine this equation with the equation F = mv^2/r to find the radius of the motion of the charged particle.
r = BQ/mv