Force due to Magnetic Fields and Currents

This is a depiction of two wires a current in the same direction. The magnetic field on the left wire due to the right points out of the board. The magnetic field on the right wire due to the left wire points into the board. This results in an attractive force between the two conductors.

Rotating a sensor around the the axis of results in a sinusoidal graph of the magnetic field.

In this experiment, we would move a bar magnet in and out of the loop of wire to see the effects that the motion had on the current. The speed at which we moved the magnet effected the current. Also, the more turns in the coil, the stronger the current.

The flux of a magnetic field through a surface.

In this experiment, we ran a current which varied over time. This created a change in the magnetic flux over time. When a toroidal solenoid with a light was placed over the rod, we see the light turn on. The changing flux induces an electric field in the solenoid. When a charge moves around the solenoid, the work done on it equals the magnitude of charge multiplied by the induced EMF. This induced emf is equal to the line integral of the electric field dotted with the total path. 

All of these factors effect the induced EMF in the situation above.

The induced emf in this situation depends only on the varying magnetic field. They magnetic field changes due the to rotation of the magnet. Taking the time derivative of the magnetic field, we end up the the formula for an induced EMF at the bottom of the board. Also, the large depiction illustrates Lenzs Law. A counter clockwise current in the coil of wires creates an upward magnetic pole. Increasing the current, increases the magnetic field, which in effect creates a current in the conductor in the opposite direction. This in effect creates a magnetic field in the opposite direction. The direction of the magnetic induction acts to oppose the cause of the effect.

When the flux is at its maximum, the instantaneous rate of change is zero, and the induced EMF is zero. When the flux is changing most rapidly (as the sinusoidal graph passes through the x-axis), the Induced EMF is at its max.