5/14/15 - Magnetic Fields to Current

Today we start by passing current though two wires next to each other. Since we know that a current passing through a wire produces an magnetic field, a force is also exerted on the two wires.

A wider angle with the power supply in view.

Given some observation points, we can use the right hand rule to figure out the magnetic field from each wire at a given point. Since we have the direction of the current and the direction of the magnetic field, we can then find the force and direction of the field. 

We substitute in for the magnetic field of an infinite line, and plug in an equation to find force.   

Now given AC currents, we were asked to predict the force acting on the wires. However, out prediction was wrong since AC currents alternate signs of potential, that means the current is alternating and therefore the net force is zero since they cancel out.

Professor's graph of a a hall sensor while rotating it and measuring the earth's magnetic field. Since the sensor is being rotated along a uniform field, the resulting graph turns out to be of sinusoidal nature.

Given our own hall sensor, a test tube, some wire, and a power supply, we hook up our setup to LoggerPro and measure the magnetic field generated by our coils of wire.

Since the magnetic field generated by the current flowing around a wire increases with each loop, we take a measurement with each coil we add to the tube.

After about 6 rough measurements, we can conclude that the relationship is more or less linear.

This fits well with our equation for magnetic moment were the amount of loops N was a linear scalar to the magnetic flux.

The graph blown up.

We were asked to find the flux on a surface parallel to the magnetic field, and since the magnetic field is perpendicular to the area vector of the plate. The dot product is zero and hence, no flux.

But when the plate is perpendicular to the field, the area vector is parallel to the field, so the dot product simply becomes the product of the two magnitudes.

An antique Galvanometer, if we could produce a magnetic field with electricity, then surly we can make electricity the other way around.

However, when the magnetic field is placed inside the coil, there is no current flow. But when the magnetic field changes, current flows.

We found that the electricity obtained from the  galvanometer was related to the velocity of the magnet, or the rate at which the magnetic field was changing.

The faster the magnetic field changed, the higher rate of change, the higher the emf was.

400 Loops

Also related is the amount of coils that the magnetic field passes through. The higher amount of coils, the more emf is produced. This is related the magnetic flux since the amount of loops has a linear relationship on the magnetic flux. And the emf is the derivative of the magnetic flux.

400 to 800 Loops

More loops = bigger EMF

Here we have metal rod with much wire wrapped around it, when we apply a current to it, it will create a large magnetic field directed upward.

Since there is a magnetic field directed upwards, we can place some wire in a coil around the magnetic field. Since there is a magnetic field, it will cause current to flow in the wire, and therefore lightning the light bulb on the loop since current is passing though the bulb.

We notice the bulb grows dim as we move it upward, this is due to the weaker magnetic field from the coil below, as the distance increases, the magnetic field approaches zero.

But since current flowing in a loop will generate a magnetic field on its own, it will then oppose the field that gives it the current in the first place.

When we empower the coil, the field generated by the coil allows current to flow in the copper piece, which in turn causes a magnetic field in the opposing direction. The opposing magnetic field causes a force, since the coil is stationary, the force is directed upwards and levitates the copper coil until the field becomes weaker and the coil reaches equilibrium.

We now put a aluminum ring on and since aluminium is might lighter than copper, the sudden change in force had launched off the coil. 

Now a steel rod is placed and it barely lifts off the surface since steel is much more dense than copper and aluminum.

It makes it almost the same distance as the copper since it is much thinner though.

Here we have a steel ring but with a discontinuity in the ring. Since there is no current flowing, there is no magnetic field and the ring remains stationary.

Since we can see changes on to the emf when we change certain parameters. We state 4 things that could affect the emf produced by the coil and magnet.

The number of coils of wire, size of the magnet (magnitude of field), how fast the magnet moves (field movement speed), and how much area is in the the loop.

Here we have the diagram of the the coils and the ring that was placed on top. Since the current was counterclockwise, the force and magnetic field is directed upward. The opposing force has to point downward, and therefore the current in the loop must flow clockwise.

Here two masses are dropped through tubes. A magnet is dropped through the aluminium tube and has a much slower drop. 

We explain this as the magnet drops, the magnetic field is changing. This change causes a current to flow in the tube, which in turn creates a magnetic field to oppose the drop of the magnet. This causes the magnet to have a much slower decent than normal.

Since magnetic flux is just the product of the magnetic field and the area, and the field is a function of the angle and time, we can write the flux as a function of time.

After we substitute some equations in, we can find the EMF as a unction of the derivative of the magnetic field times area times loops.

This is the same as just the loops times the derivative of flux, we then solved for a simplified equation.

Given a function of the magnetic field as a function of time, we can find the emf as a function of time since the derivative of sine is cosine. And constant shift is lost and the graph really only gains an amplitude change and a phase shift.

5/12/15 - Magnitude Cont. and Faraday's Law

Today we start out by creating another paperclip magnet and we attempted to destroy it by heating it up.

We noticed that after heating up the paperclip...it still works.

More heat? Not enough.

Okay, magnet bork.

A picture of the paperclips atoms before and after being magnetized, When magnetized, the atoms align with the magnetic field and therefore create their own.

Below, we have the potential ways we could destroy a magnet, adding lots of energy or just giving it a big shock.

Here we have a nicely coloured practice problem with current and magnetic fields again. Given a constant magnetic field and the direction of the current, we can find the resulting forces because of it.

We can also find the net torque and since the angle is perpendicular, the cross product can just be magnitudes.

We define the magnetic dipole moment to be the number of loops times current times the are, and we set the torque equal to a function of the dipole moment. Since there was a sine component, we define it to bet he cross product.

Below is an example problem using the formula. 

The inner working of a brushed motor. There are coils and the current passes through the brushes to push the motor.

Since there is a lot of movement in the motor, the two most likely things to break in the motor are the commuter and the brushes.

Since the commuter passes the current and the brushes allow current to pass to the commuter, if either one fails from too much wear, the motor stops working.

Given this loop, we calculated the net torque acting on the system.

Here we give the a motor a push to get it started.

The brushed motor consists of two magnets creating the magnetic field and two loops which are powered by the brushes interacting with the commuter.

Once going, the potential from the power supply keeps the motor going.

Now it's time to make our own, we begin our ghetto motor by wrapping some wire around an empty Starbucks branded coffee container.

Then we secured the coil in place and made some ghetto stands for the coil.

Taping them down and putting the magnet beneath it, we sanded one wire completely and half of the other wire so we would have a force only half the time in order to push the motor.

The ghetto motor worked fine.

Examining the torques on a motor coil, we find which direction the motor will turn based on the direction of the current.

Here we have a symbolic definition of current with electron density, charge, drift velocity, and area.

Substituting in for the area:

We equate the electric field to the Hall Voltange divided by angular frequncy.

Solving for the angular frequncy, we can find the area that it coves over time t.

Now since current is writeen in terms of the Hall Voltage, we can solve for it.

- Other group's since I lost mine -

When a current is passed through a conducting path, there is a magnetic field associated with it. The person credited with the discover is Michael Faraday who discovered the properties of this magnetic field.

With current passing through the rod, we can see the compasses align with the magnetic field generated by the current.

Our prediction, which was "way wrong".

The current passing through the opposite direction, which in turn reversed the magnetic field.

With a wire hooked up to a board, we can see the magnetic field along any point in the circuit.

The fields behave how we thought, with some canceling out or strengthening other due to the placement of the wires and the current flowing through them.

An overview of the circuit.

Here we can see that if we substitute into our equation for the magnetic field with the permeability of free space, we can see that charge times velocity is the equivalent of current times differential length.

Relating the two forces based on the permeability and permittivity of free space, we can find that multiplied together, they are the inverse of the speed of light squared. With the forces, the ration happens to have most things cancel and we are left with a ratio of velocity squared and the speed of light squared.

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