Inductance

An inductor is a coil of wire which stores energy in a magnetic field when it carries current. The inductance of an inductor is defined as the magnetic flux through the inductor per unit current. Any change in the inductor leads to a change in the magnetic field it produces. This causes a change in magnetic flux through the inductor and produces an induced emf in the inductor.

The graphs for current vs time, voltage vs time and current vs voltage are shown below. The current cannot change instantaneously. The formula for inductance is shown below.

This problem required us to solve for inductance when given turns and dimensions. Since we knew the charge density of copper, we were able to find the resistance.

Here we solved for the time constant when given the inductance and resistance.

The next 3 images are in reference to an online activphysics activity we completed. 

Below you can see that the direction of the magnetic field is in the same direction as the velocity of the charged particle. 

Here we solved for the magnetic flux using the initial magnetic field, area and angle between the area vector and magnetic field vector. 

We found that as L decreases, the magnetic flux decreases because the area gets smaller. Therefore, when the area increases, the magnetic flux will increase.

The magnetic flux is also proportional to the area.

The area is proportional to the velocity because the velocity determines the rate of change of the area.

Derivations for induced emf are shown at the bottom.

The induced current depends on the direction of the magnetic flux. Induced current is proportional to the velocity, magnetic field, size of the loop and change in area. When the max current is induced, the max emf is also induced and the resistance is at its minimum.

The current and voltage relationship in terms of capacitance is exponential. The derivations are as follows:

The derivation of inductance and voltage in terms of inductance are shown. The length of a coil is directly proportional to its permeability. 

Here we solved an inductance problem.

The units for inductance are as follows:

In this problem we showed how after a long period of time, an inductor has no effect. A conductor however still acts as a resistor and drops the current. The slope of the current vs time graph is the voltage. Inductors resist rapid change in current. 

In this activity we saw how the frequency changes the graphs for emf and magnetic flux over time.

When the area decreases, the magnetic flux decreases. The flux is proportionally dependent on the magnetic field, area and rotational angle. 

An induced emf still occurs even if the frequency is zero. The induced emf is at its maximum when the plane is parallel to the magnetic field. When the magnetic field is perpendicular to the plane, the induced emf is zero. When the frequency increases, the amplitude of the emf graph increases. 

Below Mason showed the class how a charged metal rod reacts when placed into a magnetic field. Initially the rod moved away from the magnetic. Then Mason changed the direction of the magnetic field and the metal rod moved toward the magnet. 

These  2 graphs depicts a square function produced by a function generator onto an oscilloscope.

For this experiment we used a 110 turn inductor. 

We connected the inductor to an oscilloscope and a function generator in order to produce a graph of voltage vs time. 

Using the graph above and the formula from, we found the time constant and calculated the half time.

Using the half time, total resistance and the time constant, we solved for the resistance of the inductor an the number of turns within the inductor. Our calculations were very similar to the actual number of turns which was 110.

Summary:

• An inductor is a coil of wire which stores energy in a magnetic field when it carries current. 
• The inductance of an inductor is defined as the magnetic flux through the inductor per unit current. 
• Any change in the inductor leads to a change in the magnetic field it produces. 
• This causes a change in magnetic flux through the inductor and produces an induced emf in the inductor.
• We found that as L decreases, the magnetic flux decreases because the area gets smaller. 
• Therefore, when the area increases, the magnetic flux will increase.
• The magnetic flux is also proportional to the area.
• The area is proportional to the velocity because the velocity determines the rate of change of the area.
• The induced current depends on the direction of the magnetic flux. 
• Induced current is proportional to the velocity, magnetic field, size of the loop and change in area. 
• When the max current is induced, the max emf is also induced and the resistance is at its minimum.
• An induced emf still occurs even if the frequency is zero. 
• The induced emf is at its maximum when the plane is parallel to the magnetic field. 
• When the magnetic field is perpendicular to the plane, the induced emf is zero. 
• When the frequency increases, the amplitude of the emf graph increases. 
• The length of a coil is directly proportional to its permeability. 
• When the area decreases, the magnetic flux decreases. 
• The flux is proportionally dependent on the magnetic field, area and rotational angle.