Magnetic Forces, Current, Electric Motors

The magnetic field vector, velocity vector and magnetic force vector are as shown for the north and south poles of magnets.

Here we compared an ordinary pin to a magnetic pin. The magnetic pin shows how the north and south poles are lined up.

The magnetic dipole moment is found by multiplying the number of turns in a inductor, the current, and the area together.

The torque of a current loop in a uniform magnetic field is found using the following formula: 

The problem below asked us to find the torque of a current loop that is angled. 

Here we solved for the torque in a 50 turn current loop.

Below we set up a DC motor in order to study electromagnetic forces. 

The armature rotates counterclockwise with the original set up. After switching the direction of the current, the motor now turns clockwise. When we switched the magnet poles for the motor, the motor then turned counter clockwise. Since current remains the same and the poles are switched, the motor moves counter clockwise due to the change in direction of the magnetic field. This change is due to torque.

In the next activity, we took copper wire and wrapped it around an expo marker repeatedly to make a loop of wire. We secured the sides by wrapping the extra copper wire on the outsides around the looped sections. Next we let the copper loop with the two strands sit upon two bent paper clips taped securely to the table. We placed a magnet underneath the loop and connected a series of batteries to the paper clips. The loop now rotated. The current flowing through the wire, magnetic field and magnetic force cause the loop to rotate.

The next activity showed us how currents carried by magnetic fields behave. Before the aluminum rod was charged, all of the compasses pointed north. Once the rod was energized, all of the compasses pointed in the path of a circle. They formed a series of vectors in circle. This circular magnetic field is caused by the current carrying wire.

The magnetic field is inversely proportional to the distance of the wire. The greater the separation distance, the lower the magnetic field.  The magnetic field is proportional to the current. The magnetic field goes in the opposite direction when the direction of current is reversed.

Below is a close up of one of the compasses used and the Lab-Volt used in this activity.

This activity is about magnetic fields from different wiring arrangements. The direction of the current is shown. The top left curve of wire causes the magnetic fields to cancel out since they are in the opposite direction but have the same magnitude. The inner loop on the right partially cancels out the magnetic field. When the two magnetic fields add together and cancel each other out, they are following the superposition principle.

Below is a derivation for Biot-Savart's Law. This law states that current in every part of a wire contributes to the magnetic field. By integrating, we can sum up the contributions in a current carrying wire. The magnetic field is proportional to the current and inversely proportional to the distance. 

The magnetic force to electrostatic force ratio are as follows:

Summary:

• The magnetic dipole moment is found by multiplying the number of turns in a inductor, the current, and the area together.
• Biot-Savart's Law states that current in every part of a wire contributes to the magnetic field. By integrating, we can sum up the contributions in a current carrying wire. 
• The magnetic field is proportional to the current and inversely proportional to the distance. 
• When the two magnetic fields add together and cancel each other out, they are following the superposition principle.
• The torque of a current loop can be found using the the magnetic dipole moment and the magnetic field vector.