5/14 (Lenz's Law, Faraday)

Lab Day 5/14/15: Magnetic flux, Lenz Law, Faraday

Purpose: To apply Lenz's law and Faraday's Law to magnetic fields and explore the idea of induction. 

At the beginning of class, we were given two lines that have a current, a magnetic field, and a magnetic force on each. The current was predicted to go upward when the magnetic field points out of the board. When the magnetic field goes into the board on the right line, the current also goes upward using the right hand rule. Once again, force is equal to the current, length of the wire times the magnetic field. The magnetic dipole moment is used to find the magnetic field of an infinitely long wire.

Professor mason then performed the experiment by switching on the power supply causing an alternating current in the two parallel lines. There are in fact no net forces acting as there due to the alternating current. The graph created by logger pro below shows magnetic field in respect to time where two cycles of B is observed in which we can interpret the magnetic field oscillations caused by the north and south poles by applying Faraday's law.

Magnetic Field at the Center of a current loop

We found the proportionality of loops and magnetic fields by measuring the magnetic field when applying different number of loops N to it. In this experiment, we initially turned on the power which supplied a current to measure the magnetic field change due to one loop. Next, we measured the magnetic field as we increased the coiled number of loops of the insulated wire. The ammeter was used to measure the current through the wire which displayed measurements in the graph below connected to logger pro.

As a result, the magnetic field is proportional to the number of loops and the current. Therefore, the more loops, the larger the magnetic field when B is proportional to NI. 

Given the surface area ab, we can find the magnetic flux through a surface. It is seen that when the magnetic field is parallel to the surface area, the magnetic flux is zero. When the magnetic field is perpendicular to the area, we see that magnetic flux=BA=Bab.

Next we take a look at how to create a current in a coil of a wire using magnetic fields. In the experiment above, Prof. Mason used a bar magnet and galvanometer and allowed the magnet to go back and forth causing movement (changing magnetic fields) which stimulates a current seen in the movement of the meter through induction. As he stops in the center of the coil there is no change in the meter. 

There are four ways to maximize the current. If we want to maximize the current on an induced EMF we can add more loops on the coil, have a bigger loop by increasing the area, use a bigger magnet, and also move the magnet faster. 

Major points:

  (1)currents can be induced in a conductor(coiled wire) in the presence of a changing magnetic field 

Lenz's law is explored in this experiment.

In the left picture, when the metal is placed on top of the magnet, the light bulb lights up. The picture to the right shows a thin silver loop of copper of aluminum that is placed on top of the metal in which it floats when he turns on the electricity. However when this metal is cut, it would not suspend anymore.

When the north pole of the magnet is going toward a loop, the flux increases and an upward secondary magnetic field is created causing a counterclockwise current. The changing flux created by the magnetic field created by the induced emf causes the the loop to float due to the force upward.

In this part, when we place two metals inside with one made of plastic and one made of aluminum at the same time. As a result the aluminum fell much slower than the plastic.

The reason for the magnet moving slower is because there exists a magnetic field that generates a magnetic force upward. The induced current generates a magnetic field which then creates a force that opposes the induced EMF causing it to move slower.

Mathematical Representation of Faraday's Law

The picture above derives the emf and flux. We get B=B0sinwt where we can see the coil of wire with N loops and radius R, and when placed perpendicular to B a uniform magnetic field, can be identified with factors of angular and time sinusoidally. The electromotive force in the pickup coil is derived. 

Then we look at the electromotive force in respect to time in comparison to the B vs time graph. There is a phase shift seen from the original graph of magnetic field.

Conclusion: Today we applied Lenz's Law and Faraday's Law to see how we could induce a current using magnetic fields. We were able to come up with a mathematical derivations of these concepts to find that an EMF and flux explains the relationship between the two.