Current, Magnetic Field, Flux on loops

We started the day understanding about magnetic fields effect on each other. Two wires are placed on a holder and each given the same direction of currents. The wires will push each other and jump towards a different direction. This is caused by force moving alternatively on the wires, which pushes the wire away from each other. 

When current is moving in a different direction, nothing happened to the wires because the forces cancel each other as the current alternates.
We then use a hall effect meter to prove that magnetic field is sine graph. When the sensor is turned clockwise, the graph shown in logger pro as in green below. When the peak reaches the highest (positive), it shows that the magnetic field points north. When the peak reaches the lowest (negative), it shows that the magnetic field points south.

We use the hall effect meter to see the effect on loops on magnetic field. We started making 1 coil on the sensor and add 1 loop until we get 5 loops in total.

The graph is shown below from 1 loop to 5 loops respectively. As we can see, the line increases as we add more loops to the hall effect meter.

When we place a surface vertically and have a magnetic field perpendicular to the surface area, we can find the flux to be multiplication of magnetic field and area or the sides. When the surface area is rotated and placed horizontally where magnetic field is parallel to the surface area. The flux is zero.

Next, we have 2 different pipes, one is made out of aluminum, and the other made out of acrylic. We will let 2 different masses, magnetized and unmagnetized, run throught it. When we place the magnetized in the acrylic and the unmagnetized in the aluminum, they fall at the same rate. When switch the place of the masses, the magnetized mass falls at a much slower speed than the unmagnetized mass. Just like the levitation experiment earlier, the magnetic field of the mass is pointing downward while the magnetic field of the pipe is pointing upward. But there is a gravity helping the mass to go down, so it does not stay in equilibrium and eventually falls off.

We then learn about the relationship between electric field and magnetic field. Electric field is equal to multiplication of velocity and magnetic field and it is also voltage per length. We also know that electric field is multiplication of voltage, length, and magnetic field.

Solenoid:

The apparatus has wire looped covering the bottom part of metallic pole. The wire is connected to the power. We place different type of metals and see the result when we let the power run through. First, we use copper ring. The ring levitates about half way when the power run through. Second, we use aluminum ring, the ring jumps right out of the pole. This is caused because the aluminum ring is so much lighter than copper ring. Third, we use the flat aluminum ring, it also levitates at a lower current. Lastly, we try a flat aluminum ring with a tiny cut off on it. The ring does not levitates because current cant go through it since there is a gap in the ring.

The ring lecitates because there is a different direction of current on the ring and on the wire. On the wire, the magnetic field is going upward, where else on the ring, the magnetic field is going downward, making the ring stay in its equilibrium.

We then asked what can affect the magnitude of the current in that experiment. The answers are as below:

Galvano Meter:

This apparatus reads current, just like ampmeter, but this apparatus is so much older. First, we connect the wire to the galvanometer and make a loop on the wire. Before the wire is magnetized, the meter reads zero. Then we obtain a magnet bar and insert it into the loop. The current is now read on the galvanometer. This proves that current can be generated wirelessly using a magnetic field.

We concluded that from the experiments, they follow the Lens' Law, which is induced Emf always opposed the inducing Emf. We now learn that Emf is -NA*dB/dt. From this equation, we can integrate them and find magnetic field to be -(emf)t/NA, but this equation can be equated to multiplication of initial magnetic field sin(omega*t). From this, we find emf to be -Bo*NA*sin(wt)/t. We can also replace flux with this magnetic field equation and to be Bo*sin(omega*t)A.