Electromagnetic induction (2)

Electromagnetic induction

Important factors in inducing currents

• 1. An emf is induced if the coil or the magnet (or both) move (change in flux).

• 2. The size of the induced emf depends on the speed of movement.

• 3. The induced emf depends on the strength of the B field.

• 4. Changing the area inside the magnetic field

• 5. Increasing the number of turns also changes the flux linkage, and so induces a greater emf.

What you are going to learn today

• What is magnetic flux, and magnetic flux linkage?

• What must happen to a conductor (or to the magnetic field in which it’s placed) for electricity to be generated?

• What factors would cause the induced emf to be greater?

• What is Lenz’s law and what are the applications of this law?

Flux - The rate of flow of energy through a given surface

• flux density B (The strength of your magnetic field)

• magnetic flux, . rea

• Flux Linkage, N – (N = number of

turns)

Lenz’s Law

• Lenz’s Law states that the direction of the induced current is always such as to oppose the change that causes the current.

• To include this idea in our formula, a minus sign has to be introduced, giving;

•             Emf = – N x d/dt

Fleming's Right hand rule

p133

Kinetic energy recovery systems

Toyota• http://www.youtube.com/watch?

v=evZ-C8fVrP4F1

• http://www.youtube.com/watch?v=09knBT2gqqU

Inducing an Emf (no current yet)

• Connect the coil of wire to the micro-voltmeter and place it close to the magnet.

• 1. Move the magnet next to the coil. What happens? How does it depend on speed and direction of movement?

• 2 .Move the coil next to the magnet. What happens? How does it depend on speed and direction of movement?

• 3. Gradually unwind the coil in the magnetic field. What happens?

• 4. Take the coil and crumple it up, keeping it in the field. What happens?

Conductor in a magnetic field

Metal rod, length L in a magnetic field moving with a velocity v down the page.

An electron in the rod will experience a force (= Bev) that will push it towards the

end Q

The electrons will be pushed towards end Q leaving end

p more positive

an electric field E builds up until the force on electrons

in the rod due to this electric field (= Ee)

balances the force due to the magnetic field.

Ee = Bev so E =BvFor a rod of length L,

E = V/L and so V/L = BvHence the induced emf = BLvv = velocity E = Electric field

V = Voltage B = Magnetic field

Completing the circuit• The emf will now cause a current to flow in

the external resistor R. This means that a similar current flows through the rod itself giving a magnetic force, BIL to the left

• L is now the separation of the two conductors along which the rod PQ moves.) An equal and opposite force (to the right) is needed to keep PQ moving at a steady speed.

• The work done in moving the rod will equal the energy dissipated in the resistor.

• In a time t, the rod moves a distance d = v t

• Work done (FxD) on the rod = BIL v t

• Energy dissipated in R = power x time = ItV

• giving BIL v t = ItV

• Emf (V) = BvL

However! You are increasing the area inside the magnetic

fieldEmf (V) = BvL

In one second the area has increased by Lv (A =Lv)

induced emf = B x area swept out per second

= B x A / t

B x A can be called the magnetic flux, .

Thus induced emf = / t = rate of change of magnetic flux

And more generally emf = d / dt

So how can you increase the induced voltage?

L

Flux Linkage (N )

• Increasing the number of turns of wire N in our circuit increases the emf produced

• induced emf   =   rate of change of flux linkage

•  emf = N x d/dt

Sketching Flux Patterns

NSNS

SN

– +