When a current flows through a conductor in a magnetic
field, it experiences a force. 

The relation between the directions of the current, field and force can be
remembered by using Fleming's left hand rule. 



Anybody who has been paying attention and has understood the significance of
Lenz's law might not be surprised to find that, for the situation in which
we move a conductor through a magnetic field in order to generate an emf, an
opposite rule can be used. 

Can you guess what it's called? Yes...
Fleming's right hand rule! 





The aid to memory is the same but remember to use your right hand
this time. 

As always in electromagnetism, we are again talking about conventional
current. 



Consider a coil of wire, rotating in a uniform magnetic field, of flux
density B as shown below. 



When the coil is in the position shown in the diagram,
side 2 is moving down and side 1 is moving up. 

We can use Fleming’s right hand rule to decide that end q
will (at that instant) be the
positive terminal of the generator. 

Remember, when using the rule, that conventional current flows
away from positive towards negative outside the source of
electrical energy, the generator in this case. 

When the coil has rotated through half a turn, and p will be
positive. 

Therefore, a coil rotating in a uniform magnetic field will have
an alternating emf induced in it, of frequency equal to the
frequency of rotation of the coil. 

To connect the coil to, for example, a light bulb, carbon
brushes make contact with brass slip rings as shown in
the next diagram. 





Let the coil have N turns. 

The flux density has magnitude B. 

The crosssectional area of the coil is A. 

Let the angle between the normal to the plane of the coil and
the field be α 

Then the flux linkage between the field and the coil is given by 



If the angular velocity of the coil is ω
then
α=ωt 

This is assuming that at t = 0, the
plane of the coil is perpendicular to the flux lines, ie at 90° to
the position shown above. 



So, using the FaradayNeumann law we have 



The term 

in the above equation, represents the slope of a graph of cosωt
against t. 


and, it can be shown that the slope of a graph of cosωt
against t is equal to ωsinωt 

Therefore, the induced emf in the coil is given by 



This means that a graph of induced emf against time would
look like this 





Below the graph are the positions of the coil relative to the magnetic field
which correspond to maximum induced emf and zero induced emf. 
