PhysicsLAB Worksheet
Induced emf

Introductory Information
 
When working with inductors in problems, it becomes necessary to determine the direction of the induced emf in a coil (solenoid). Here are some examples of the type of situations with which you should become comfortable.
 
The inductor in all of the examples, is wrapped so that the wires come "down the front" and "up the back" like the coil shown on the left. If the current generated by the circuit changes, then the magnetic field in the solenoid changes and the flux through the coil will change. Remember that the coil ALWAYS reacts to oppose ALL changes in flux lines by inducing an emf that will counter the increase or decrease - thus creating a latency, or inertia.
 

By Zureks (Own work) [Public domain], via Wikimedia Commons
Refer to the following information for the next three questions.

The circuit contains a battery having a constant voltage, a coil, and a variable resistor. The current in the circuit is flowing clockwise.
 
If the variable resistor's resistance remains constant, in which direction would an emf be induced in the coil?
 
If the variable resistor's resistance is suddenly decreased, in which direction would an emf be induced in the coil?
 
If the variable resistor's resistance is suddenly increased, in which direction would an emf be induced in the coil?
 
Refer to the following information for the next two questions.

In this section, the battery has been reversed, so current in the circuit is flowing counterclockwise. The solenoid and variable resistor are the same as those used in the first section. Since the current has now been reversed, note that the north pole of the electromagnet (solenoid) is now pointing towards A.
 
 
If the variable resistor's resistance is suddenly decreased, in which direction would an emf be induced in the coil?
 
If the variable resistor's resistance is suddenly increased, in which direction would an emf be induced in the coil?
 
Further Background
 
As seen in the previous problems, the solenoid (or inductor) acts to resist any changes occuring in the magnetic field flux produced by the current that is passing through its loops. Remember that an emf is ONLY induced when there is a change in the flux; moreover, it is as if the inductor acts as a "temporary variable battery" whose orientation opposes the flux change.
 
The degree to which it provides resistance is called its inductance, L. The emf produced by the inductor is calculated with the formula .
  • So, if the current is decreasing,  , the induced emf in the loops will be positive syncing the inductor with the direction of the battery so as to temporarily attempt to replace the decreasing flux through the inductor.
  • Conversely, if the current is increasing, , the induced emf in the loops will be negative which reverses the inductor's emf with that o the battery so as to temporarily attempt to decreases the increasing flux through the inductor.
 
 
NOTE: if you did not view the solutions to the previous problems, do so now so you can visualize how the conditions pair together.
 
Refer to the following information for the next two questions.

We are now going to calculate some numerical values for the inductance of a solenoid and induced emf. To determine the numerical value of the geometric inductance of a solenoid we will use the equation  where
 
  • N is the total number of loops (coils)
  • is the length of the solenoid
  • A is the cross-sectional area of the solenoid's core
  • µo is the permeability of free space (or in our case, air)
 
Also recall that inductance, L, is measured in Henries where 1 H = 1 volt per (amp/sec). Another definition of this unit is 1 H = 1 weber of flux per amp of current.
 
 
For the solenoid used in the previous sections we now are given that it has a total number of 2000 loops (or turns of wire), its length is 16 cm, and its cross-sectional area has a diameter of 6 cm.
What is the geometrical inductance of the solenoid? 

If the battery has an emf of 40 V and the resistance of the resistor is changing according to the equation  what emf will be induced in the solenoid at t = 4 seconds? 





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