Magnetic Fields Tutorial 2 - Coils in Magnetic Fields

In the diagram below, we have a coil of wire, of n turns, suspended vertically in a magnetic field of strength BIt can rotate around the vertical axis.



A current I passes through the coil.  We will look at the coil from above.  If we set the coil parallel to the field, we will get this:

The w term is the width of the coil. The n term refers to the number of turns on the coil.


The sides AC and BD are vertical, and will experience a force:


F = n(BIl)


The torque on the couple is given by:

G = Fw


The strange looking symbol, G, which looks a bit like a gallows, is “Gamma”, a Greek capital letter ‘G’.  It is often used as the Physics code for torque.


Now the coil is at an angle q:



Because the force F is always at 90o to the magnetic field, the distance between the lines of action of the forces, d, reduces.  Therefore the resultant force reduces:


G ′ = Fw cos q = BIlnw cos q




Since length × width, lw, gives area, A, we can now write:


G ′ = BAnI cos q


When the coil is at 90o to the field, cos q = 0.


The bear-trap here is to think that the side AB is being acted on by the magnetic field.  Remember that the force is acting on the vertical wires, AC and BD.  We are looking down at the coil from above.  The wires running between A and B (and C and D) are parallel with the magnetic field.  Therefore they experience no force.



The main application of this is with the electric motor.  The universal motor is found in a variety of different household appliances.  This one is from a vacuum cleaner.


 Photograph by Marrrci from Wikimedia Commons.  Captions translated from the original German.


 Each of the coils is connected to the outside circuit by a split-ring commutator and spring-loaded carbon brushes.


Notice that the field magnets are curved.  If the field is radial, the angle that the coil makes with the magnetic field is always constant at 0o.  In other words, the coil is always parallel to the magnetic field lines through which it is turning.  Therefore F remains constant, and the torque remains constant.



The Electric Motor

This motor works on direct current.  You may well have made something similar in class



The current is carried to the armature through carbon brushes and a split-ring commutator.  The commutator acts as a change-over switch so that the current on the left hand side of the coil always moves towards us (and on the right hand side, away).



The armature turns through 90 o and the force is zero.




In this case, we see that the armature is at 90 degrees, so that the current is at 0 degrees to the field.


There is zero force, and the motor stalls.


To prevent this, small DC motors have 3 poles so that at least 1 pole is providing a force.  The motor keeps on turning.  If we reverse the current, the direction of the rotation changes as well.  In larger motors there are several coils.



In this simple alternating current motor there is a permanent magnet that turns between two coils:



This motor has a cylindrical magnet (from an old pond pump) which is mounted on a shaft held by clamps mounted on clamp-stands.  There are coils connected in parallel, connected to an a.c. supply.  Changing the voltage does not affect the speed of the motor.  In most a.c. motors there is no permanent magnet.  Instead there is a magnetic field induced in the rotor by the alternating current.  Such a motor is called an induction motor.  It does not work on direct current.  The picture below shows a small induction motor on a bench drill.