# Induced current in parallel loop

#### bluedevil09

1. The problem statement, all variables and given/known data

The drawing below shows a circular loop of wire (raadius 0.15m) connected to a power supply. The top loop is directly over the bottom loop, which is not connected to anything.

In the picture, the loops are shown parallel with one over the other, with the perspective looking at an angle from the top. When looking from the top, the negative terminal is connected to the top loop, which then loops around CCW to the positive terminal.

A) When the switch is first turned on, in which direction will the current first flow in the bottom loop?

B) The bottom coil receives a constant magnetic field of 0.8 T from the top coil and starts spinning perpendicular to its original plane at a speed of two revolutions per second. Find the average emf induced in that coil as it rotates through one-fourth of a revolution.

C) If the bottom loop begins rotating away from the viewer (the near part of the loop begins to move down), which direction is current first induced in that loop?

2. Relevant equations

for B: V = N*B*A*w*sin(theta)

The others are just going to be drawings I believe

3. The attempt at a solution

A) Using RH rule, the field is going to point upwards. I believe that the current would therefore flow the same direction in the lower loop, but I'm not sure if I need to factor something else in.

If someone could just help explain to me how to figure out part A, that would be a great start. The online class I'm taking does not explain Lenz's law hardly at all, so I am not really sure how to do this. I'll move on to the other parts after I get this one.
Thanks!

#### Delphi51

Homework Helper
Lenz's law says the field due to the induced current will oppose the original field. No doubt you have seen the demo of dropping a magnet through a copper tube where the opposition reduces the speed of the falling magnet. If it were the other way round, you would be driving a car powered by a perpetual motion machine.

So the current has to go the opposite way around the lower loop. When answering, be aware of your class convention - is it electron flow or conventional positive flow.

#### Kruum

Lenz's law says the field due to the induced current will oppose the original field.
I've been trying to figure out the directions, the Lenz's law state, as well. So if we take a loop of wire, like the one in this case, doesn't the upper loop itself then induce a magnetic field that's trying to oppose the field created by the current. So when determing the direction in the lower loop, which field we take into consideration and why?

Edit: Does the induced field always have smaller magnitude than the created field? If, so then we obviously need to consider only the field created by the current.

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#### Delphi51

Homework Helper
This is a bit beyond my knowledge, but yes, I would expect the increasing magnetic field would induce an emf in the loop that caused it, and this emf must oppose the original current. This is the effect that gives a coil reactance so a transformer primary is not a short circuit for AC current.

#### Kruum

This is the effect that gives a coil reactance so a transformer primary is not a short circuit for AC current.
Yeah, that's what also ran through my mind. And since there is some current running through an inductor, or a coil, in an AC circuit, the induced field then is smaller than the one created by the current.

#### bluedevil09

Wow... thank you! That is pretty easy to understand. For part B, I can figure out everything in the equation I put (with w being angular velocity = 2pi*2, N being loops = 1, A being area = pi*0.15^2, B being magnetic field = 0.8T, and theta = 90 - for quarter of a turn). This gives me the emf at 1/4 turn though, correct. If so, would the average be half of my answer?

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