# What is the direction of induced current

1. May 24, 2015

### nawand

1. The problem statement, all variables and given/known data
Use Lenz’s law to answer the following questions con-
cerning the direction of induced currents. Express
your answers in terms of the letter labels a and b in
each part of Figure P31.22. (a) What is the direction of
the induced current in the resistor R in Figure P31.22a
when the bar magnet is moved to the left? (b) What
is the direction of the current induced in the resistor
R immediately after the switch S in Figure P31.22b is
closed? (c) What is the direction of the induced cur-
rent in the resistor R when the current I in Figure
P31.22c decreases rapidly to zero?

2. Relevant equations
F=I L x B

3. The attempt at a solution
By looking at the picture "a" we see the poles of magnet pointed to the right, so the magnet field would be to the right on the coil, this is only possible if the current would pass clockwise. Since the magnet is leaving to the the left, the flux is decreasing. The system responses by creating a magnet field that compensates its leaving so the direction of current in the coil would be clockwise. Which is opposite to the answer sheet.
By b is either not sure whether solutions are good. Whenever switch is closed the flux will be increased so the magnet field pointed to the right. The system responses by opposing these increasing. The only way to do this is to send an induced current from b to a in the resistor.
c is good!
Hope someone corrects me if there is anything wrong,
Thanks

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2. May 25, 2015

### rude man

What do you mean by "clockwise"? You're supposed to give the direction of current in the resistor using labels a and b.
(b) I would look at again.
What do you mean by "c is good"? What is your answer?

3. May 25, 2015

### nawand

Question a)

The magnet field is pointed to the right, when you move the magnet, there will be a current created in the loop which is from a to b Since the field is decreasing, the induced current will replay the direction of current which is from a to b: (Counter-clockwise) (Apparently I had my answer posted mistakenly)
I assume there is well an ambiguity since
• Field in the coil is to the right
• Field in the resistor also to the right (Also a closed loop)
By considering the field created in the coil (the upward part of the system), the direction of the current will be from b to a in the system and resistor as well, which is clockwise in the whole system (If you look on page as a clock). By lowering it the system will create the same direction, so the answer is not that in the answer book.

By considering the magnet filed in the resistor (I think this was intention of the author) the current will be directed to the right which is from a to b, then the induced current will be also from a to b, since it will oppose the decreasing of field by continuing its direction. In this case the answer is right.

Question b)

Switching the loop on, you will make a potential difference so the direction of current is from "+" to "-", which is again clockwise (if you look on page as clock) regarding the loop as a clock (Only if "+" and "-" signs in the book are not mistakenly replaced). This will create a magnet field which is the changing of a flux from zero to a positive value pointed to the right regarding to a second coil where a and b exist. This second coil will oppose this change by creating its own magnet field directed to the left. This is only possible if the current will be circulating from a to b in the loop or from b to a in the RESISTOR. In this way surely in the answer book something is missed. Because I can't direct a current from a to b in the resistor having a magnet field to the left to oppose the created magnet field by the coil to the right.

The only explantion can be mistakenly depicted signs of "+" and "-" in the question which is consistent with the rest of book where longer part is "+" not "-"

Question c) I thought its is obvious since lowering the current will makes system to oppose create a magnet field in the direction it was, this was into the page (right hand rule). So the lowering the current in the wire, the loop would have an induced current (clockwise if you look as a clock on the page) which is from a to b in the resistor. Which I said Good (meaning is correct in the answer book).
Thanks for reading my post,

.

4. May 25, 2015

### theodoros.mihos

Lenz's law is$$\epsilon = -\frac{\partial\Phi}{\partial{t}}$$

5. May 25, 2015

### rude man

Correct. Avoid the use of 'clockwise' & "counter-cw". Makes no sense.
You are right about the unconventional + and - signs on the battery. Get this resolved first.
Correct.

6. May 25, 2015

### nawand

Thanks a lot!
This makes me sure I understood it. "You learn only if you get right feedbacks".

7. May 25, 2015

### rude man

You are very welcome!