Inductors

We started the day answering questions on the active physics website. Given a loop as shown below, we anwered the questions as below. Using the program, we can answer the questions as below

These questions help us understand of the relationship between flux to magnetic field, force, current

Recall about the right hand rule that we learned in the past lectures connecting force, magnetic field, and current. Given a setup as below, the current goes through the tube metal from the side thats closer to us, with magnetic field going from north to south, which is pointing upward. This means that the force is going away from the magnet. When we let the current run through, the tube metal rolls over away from the magnets and fell from the table, which proves that our prediction was correct. When we switched the positive and negative sides of the metal, which causes the current to go through the opposite way, the tube metal rolls closer to the magnet.

We then do some more questions. Given a loop as shown below, we again anwered the questions as below.

Understanding inductors:

We learned that inductor is flux per current. It works the same was as capacitors because they both store energy. When voltage increases, current decreases. When magnetic field increases, back emf is also increasing. The more number of coils also increases the resistance of it.
Inductor is also emf produced by the inductors divided by dI/dt. Using the algebra, we found dI/dt to be the emf/inductor. We know that emf is in voltage; thus, voltage is inductors multiplied by dI/dt.
Capacitor can also be related to the time, by replacing charge with multiplication of current and change of time, we find current to be I*change of time per voltage.

The equations below are some of the already simplified equations from the laws that we have learned before.

We knew from past lecture that flux is multiplication of number of loops, magnetic field, area vector, in an angle of cosine. We can replace magnetic field with myu, number of loops, divided by the length. When we integrate them, we find flux to be that multiplied by the time. When we derive the equation in terms of time, we found the equation to be in dI/dt. Recall that voltage is induction multiplied by dI/dt, we can replace voltage to this and get rid of the derivation. Finally, we found the induction to be myu*N(square)*A/l.

We are then given a question with known radius of 0.1 cm, number of loops 100, length is 4 cm. We know that magnetic permeability of copper is 1.26 * 10^-6. First, we convert all the units into SI units, so the radius and length would be in meters. Using the equation that we derived, we just plugged in all the known and found the answer to be 9.9*10^-7.
We then learn that in DC circuit, induction has no effect. It only has effect in AC circuit. Also, we predicted the graph of voltage vs. time when current vs. time graph is a flat horizontal line. We predicted it to be a vertically straight line because  based on the equation that we know, when current does not change, resistance increases or decreases, which causes the voltage to stay vertically at a particular time.
We also learned that emf is 1/2 LI(square).

We learned about time constant in the past. Time constant is RC. When time constant foes to zero, the
Lastly, we another set of questions from the active physics website as below.