Electromagnetic induction, Electromagnetic induction, flux and flux linkageflux and flux linkage

Making Making

electricielectricityty

(resourcefulphysics.org)

It is important to grasp that

•‘‘electricity’ is only produced electricity’ is only produced while something is moving while something is moving

•the faster the movement, the the faster the movement, the more ‘electricity’ we get.more ‘electricity’ we get.

How is the ‘electricity’ made?

Flux density (B)

v

LQ

P

How is the ‘electricity’ made?

Flux density (B)

vL

Q

P

Consider a conducting rod PQ moving at a Consider a conducting rod PQ moving at a steady speed steady speed vv perpendicular to perpendicular to a field with a flux a field with a flux density B. density B.

An electron (negative charge e) in the rod An electron (negative charge e) in the rod will experience a force (= Bev) (Fleming's will experience a force (= Bev) (Fleming's left hand rule) that will push it towards the left hand rule) that will push it towards the end P. end P.

How is the ‘electricity’ made?

Flux density (B)

vL

Q

P

The same is true for other electrons in the The same is true for other electrons in the rod, so the end P rod, so the end P will become will become negatively negatively charged, charged, leaving Q with a positive leaving Q with a positive charge. charge. As a result, an electric field E builds up until As a result, an electric field E builds up until the force on electrons in the rod due to this the force on electrons in the rod due to this electric field (= Ee) balances the force due electric field (= Ee) balances the force due to the magnetic field.to the magnetic field.

We already know B is the flux densityWe already know B is the flux density and that the quantity B and that the quantity B A is the magnetic A is the magnetic flux, flux, ..

Thus induced emf = Thus induced emf = / t = rate of change of / t = rate of change of fluxflux

And more generallyAnd more generally = d = d / dt / dt

How can the induced emf (How can the induced emf ( be increased? be increased?

•moving the wire faster - dA /dt increased - moving the wire faster - dA /dt increased - rate of change of flux increasedrate of change of flux increased

•increasing the field (and hence the flux) - increasing the field (and hence the flux) - rate of change of flux increasedrate of change of flux increased

But there is a further possibility But there is a further possibility and this is to increase the number of turns of and this is to increase the number of turns of wire N in our circuit. wire N in our circuit.

By doing this, the flux has not been altered but By doing this, the flux has not been altered but the flux linkage (N the flux linkage (N ) will have increased. ) will have increased.

Hence it is more correct to say thatHence it is more correct to say thatinduced emf = rate of change of flux linkageinduced emf = rate of change of flux linkage

= N = N d d/dt/dt

= N = N d d/dt/dtThis relationship is known as This relationship is known as Faraday's law: -Faraday's law: -

when the flux linked with a circuit changes, the when the flux linked with a circuit changes, the induced emf is proportional to the rate of induced emf is proportional to the rate of change of flux linkage.change of flux linkage.

Finally, the magnetic force in a generator is in Finally, the magnetic force in a generator is in a direction which would make the bar slow a direction which would make the bar slow down unless an external force acted. down unless an external force acted.

This is an example of This is an example of Lenz's lawLenz's law: -: -

the direction of the induced emf is such that it the direction of the induced emf is such that it tends to oppose the motion or change causing tends to oppose the motion or change causing it.it.To include this idea in our formula, a minus To include this idea in our formula, a minus sign has to be introduced, giving;sign has to be introduced, giving;

= – N = – N d d/dt/dt