1.) Okay I have this problems but I can't get the picture or show the picture so i will describe it. I have two loops or circles next to each other. The first loop is continuous and there are no breaks in the loop. So it looks just like a circle. The second loop has a break in it and it also has a emf or power supply then it is a break in the circle or loop (like an open gate) then the loop continues. The current is flowing from positive to negative in a clockwise motion.

Here is the question:

Suppose you are looking at two loops in the plane of the page as shown. When the switch is thrown closed in the left hand coil, what is: a) the direction of the induced current in the other loop; b) the situation after a "long" time; c) the direction of induced current in the second loop if the second loop is quickly pulled horizontally to the right?

2.) What is the inductive reactance? (write down an expression and specify it units)

Okay i know that it is xL=wL and the units are ohms but please explain how do you derive this! and explain what it is use for!

Solution Preview

Please see the attached file.

SOLUTION

Fundamentals in a nutshell
1. When current flows through a conductor, an electromagnetic field is produced around it. The direction of the magnetic lines of force thus produced can be determined using the right hand rule as follows :

Curl the fingers of right hand with the thumb stretched out in the direction of the current flow. Then the fingers point in the direction of the magnetic field lines.

Fingers
(field line direction)

Thumb (Current direction)

2. Faraday's law : Whenever the amount of magnetic flux (total number of magnetic lines) linked with a circuit changes, an emf is induced in the circuit. The induced emf lasts so long as the change in magnetic flux continues. The magnitude of emf induced in the circuit is directly proportional to the rate of change of the magnetic flux linked with the circuit.

Thus the magnitude of induced emf e = dφ/dt (rate of change of flux)

3. Lenz's law : While the magnitude of the induced emf is given by Faraday's law, the polarity of the induced emf is given by Lenz's law. According to this law, the polarity of the induced emf will be such ...

Solution Summary

Step by step solution provided. Electromagnetic induction problems are examined.

See attached lab report file.
Please complete the graph for Step 9 under procedures (a graph of Primary Current vs. Galvanometer Deflection using the data from Steps 6 and 7) and provide results and conclusions.
Please answer the four questions, the optional question and exercise.

A metal ring 4.80 cm in diameter is placed between the north and south poles of large magnets with the plane of its area perpendicular to the magnetic field. These magnets produce an initial uniform field of 1.12 T between them but are gradually pulled apart, causing this field to remain uniform but decrease steadily at 0.210 T

A constant magnetic field passes through a single rectangular loop whose dimensions are 0.35 m x 0.55 m. The magnetic field has a magnitude of 2.1 T and is inclined at an angle of 70° with respect to the normal to the plane of the loop.
(a) If the magnetic field decreases to zero in a time of 0.52 s, what is the magnitud

A coil of wire with 40 turns is held stationary between the poles of an electromagnet. The field in the electromagnet is increased from 0 to 0.75T in a time of 225 seconds. What is the magnitude of the induced EMF in the coil if the angle that the plane of the coil makes with the field is 30 degrees?

A natural satellite whose diameter is 10^4 meters moves at velocity of 1 km/s in the direction normal to the magnetic field of a planet in a region where B=10^-7 Tesla. The satellite has appreciable conductivity.
d) Someone suggests that this current could provide power for an artificial satellite traveling in the same dire

A potential difference of 0.050V is developed across the 10 cm long wire as it moves through a magnetic field at 5.0 m/s. The magnetic field is perpendicular to the axis of the wire. What are the direction and strength of the magnetic field?

Let f:N x N -> N be the function defined recursively as follows:
f(0, 0) = 6
f(i, j) = f(i - 1, j) + 2 if i > 0 and j = 0
f(i, j) = f(i, j - 1) + 1 if j > 0
Use induction on the sum i + j to prove that f(i, j) = 2i + j + 6 for all (i, j) in N x N.

** Please see the attached file for the full problem description **
16. Which of the following expressions is correct for the transmitted intensity of an unpolarized beam of light with an intensity Ii passing through a polarizer
17. A certain part of the electromagnetic spectrum ranges from 200 nm to 400 nm. What is the hi

Hello,
Can you please assist with the induction step for this problem?
3. Prove that
1 + 2 + 2^2 + ... + 2^(n-1) = 2^n - 1
for every n > 1.
5. Prove that for any real number x and for all numbers n > 1,
x^n - 1 = (x - 1)(x^(n-1) + x^(n-2) + ... + x^(n-r) + ... + x + 1).

Please see the attached file for the fully formatted problem.
Without using Theorem 4.2.2, use mathematical induction to prove that
P(n): 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1) for all integers n >= 1