Cathode Ray and Oscilloscope

Cathode Ray:

We started the day understanding about cathode ray. The way it works is

Next, we learn about Cathode Ray Tube. In it, there is a mechanism that emits electrons. First, the emitted electrons are concentrated into a tight beam by thr focusing plate. Right after, the electrons are subjected to different plates that alter their x, y axis positioning by using electric potential difference.

We learned a force in electron from past lecture that m*a in electric is q*E. These two understanding can be equated and we can find acceleration to be qE/m. But electric field we know to be V/d. The electric field can then be replaced, so the equation is qV/dm.

From 4A we learned that y is Vx*t. When we substitute this to the equation of acceleration we found earlier, we can find the time to be qVLD/mdV(square).

Oscilloscope:

We follow the instructions exactly as the lab manual says to familiarize ourselves to the use of oscilloscope.

Second, we switch over to sinusoidal wave and square wave outputs of the fuction generatur. Square wave comes out as below:

Sinusoidal output comes out as below:

The function generator is then hooked up to channel 2 of oscilloscope. When both function generators have same frequencies, it will create a circle as below.

When both function generator are given 180 Hz, it shows as below.

We are then given a box and we had to determine the type of current from the oscilloscope by using AC and DC.
When we used red and black AC, it comes out as below:

When we used red and black DC, it comes out as below:

When we used Black and Green and Black and Blue DC, it shows as below:

When we used Red and Blue and Red and Green DC. it shows as below:

When we used Red and Yellow (DC and AC), it shows as below:

When we used every other combination of colors (DC and AC), it shows as below:

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.

Magnet and Electricity

We started the day with understanding the difference between unmagnetized object and magnetized. When an object is unmagnetized, it contains a positive and negative poles that are all over the place. When the object is magnetized, the poles are ligned up.

We know that an unmagnetized object can be magnetized, but can it be the other way around? We then pedicted that it can be by using heat, forceful contact with similar pole, or by hitting it with a hammer. Then, we confirm the first prediction by heating a magnetized clip. When we heat it long enough, the clip becomes unmagnetized and is not able to pick up a metallic object anymore.

We learned about the foce in magnetic field in the past lecture, now we learn about torque. Given a diagram as below in green, we want to first predict the force. When current is going to the right, the force is facing towards us and when the current started to go to the left, the force is going away from us. But when the current is parallel to the magnetic field, as we learned before, the force is zero. We knew from phys 4a that torque is r x F. In this diagram, r is half of the given length. Thus, by substituting the equation into the force equation, we found torque to be 1/2 IL(square) x B. The L(square) is Area, so it can also be replaced by Area in the equation.

Multiplication of number of loops, current, and area is also a myu, therefore, we can also use myu x B for a torque equation.

Given known as below, we want to calculate the torque. In a circle, area is pi*r(square), by replacing the area and plugging in the knowns, we find the torque. But we needed to be careful with angle. The angle given is between the field direction and plane of loops, the angle in this equation is the surgace area perpendicular to plane of loop.

A motor has some problems that can fail along the way. Those include the brush in the commutator and the coil. 

Given another problem as below, we have current, nunber of loops, radius, and magnetic field. By plugging in, we can again find the torque as below. The angle in this problem though is 90* because the area is perpendicular to the loop.

We then learn how a motor works with batteries and magnet. The commutator is placed perpendicular to the magnet with different poles placed on each sides. The north pole connected to the positive side of the battery and the south pole connected to the negative side. When the commutator is let go, it keeps on spinning to the clockwise from north towards the south pole as shown below. When the cable is switched for the north to be connected to negative side and the south connected to the positive side, the commutator spins counter clockwise. When the magnets are switched with the same setup, the commutator spins clockwise as the first setup and when the cable switched again, the commutator spins counter clockwise again. When the magnets are on the same poles facing each other or when the magnets are removed, the commutator does not spin at all. This shows that the magnet is needed for the motor to work.

We learned about relationship between current and velocity drift. We now want to find the relationship between current and velocity h. We learn that electric field is multiplication of velocity drift and magnetic field. We also learn that electric field is velocity h per work. By equating these equations, we find velocity drift to be velocity h divided by work and magnetic field. Using this equation, we can replace velocity drift and find current to be multiplication of density, charge, velocity h, and time per magnetic field as shown below.

A pole with a current is connected to a power source. We then place compasses around the pole. At first all compasses pointing north, which is placed in a clockwise manner. When the power is turned on, all compasses pointing south or counter clockwise as seen in the picture below. This shows that ...

Last, we tape a cable on a board with a setup as below. By connecting each ends of the cable to a power, the current goes through the cable from negative to positive.

We then learn that the ratio of force of magnetic field and electric field is multiplication of epsilon, myu, and velocity(square), but we knew that epsilon is inverse of myu and capacitor(cube). By replacing it, we found the ratio to be velocity(square)/capacitor(cube).

Lastly, we learn about ampere's law. Integration of magnetic field and change of length is equal to myu multiplied by current inclosed.

Magnet

We started the day understanding about magnets. A paper clip does not have a magnetic charge. When it is given magnetic charge by being placed in a horseshoe magnet and cut into half, the magnetic charge is shown by using a compass. The compass moves when the paper clip is moved closer to it.

Understanding Magnetic Field:

Magnetic field is the magnetic vector space in which the forces movement around a magnet can be seen. The force moves from north to south pole of the magnet. Apparently, the drawing below by Adrian is falsely drawn and he didnt change it :( 

When you draw the magnetic field, it will follow the arrows drawn as before. This will look like a rainbow jumping from the north pole to the south pole of the magnet. 

This is a horseshoe magnet. It's just like a normal magnet, but the poles are bent to get closer to each other, so both north and south pole are on top.

We learn that flux is the number of poles enclosed. The formula for this is magnetic field times Area, which is also net nunber of poles enclosed per epsilon.

We also learn that the units known for magnetic field are tesla and gauss. Gauss is 

Understanding relationship between Force, magnetic field, velocity:

When we move a magnet towards a oscilloscope, the bright dot in oscilloscope move to a certain way. When the magnet is moved closer from the top of the oscilloscope with the north pole pointing downward, the dot moves to the left. This shows the direction of Force. Using right-hand rule, we can figure out the direction of velocity as shown on the first picture below. We can also predict the direction of Force and velocity when the south pole of magnet is brought close to the oscilloscope using the same method. We found the Force to move to the right and velocity is moving away from us. When north pole of magnet is moved closer on the sides of the oscilloscope, the force moves downward and moves upward when south pole is moved closer. Lastly, we try to move the magnet inward/outward, we found that there is no movement in the Force. Thus, we conclude that Force is zero when magnetic field is parallel to the beam. This right-hand rule only applies for protons, whereas electrons will use a left-hand rule.

We then learn that Force is a cross product of charge and velocity by the magnetic field. By deriving it, we can find the magnetic field units to be kg/Cs, or is also known as N/A.m

Given the value of magnetic field, velocity, charge, and angle. We can calculate the magnitude of force by using the formula that we just learned and found the force to be 6.24* 10^-16 N as below. We also We can then find the acceleration using the mass of the proton that we know ti be 6.67* 10^-22kg. Using the newton's second law, we found the acceleration to be 9.35* 10^10 m/s(square).

Understanding Magnetic Field in Charged Wire:

For our next eperiment, we will place a wire horizontally in between the horseshoe magnet. When the wire is given charged, the wire jumps up. This shows that 

We knew from phys 4A that radial force is mv(square)/r. We can set this equation equal to the equation force that we just learned. By deriving these equations, we can find r to be mv/q x B.

Velocity does not only move in a straight line, it can also move radically. The direction of velocity can still be found by using the right hand rule. This velocity is positive when moving in clockwise direction and negative when moving in counter clockwise direction.

We can find a magnetic field from a known frequency. Recall from phys 4A that omega is v/r, which we can use to replace velocity in the magnetic field equation from earlier. We found the magnetic field equation to be m*omega/charge. We also know that omega is 2*pi*frequency. Thus, we can calculate the omega, then plug it in to find the magnetic field.

Understanding Magnetic Field in Charged Coiled Wire

For our next eperiment, we will place a coiled wire horizontally in between the horseshoe magnet. When the wire is given charged, the wire jumps 90*. This shows that