• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Flux in a Wire Loop w/ a Magnetic Field

1. Homework Statement

Diagram: http://img.photobucket.com/albums/v696/talimtails/PP24.jpg

A wire loop, 2 by 4 meters, of negligible resistance, is in the plane of the page with its left end in a uniform .5 T magnetic field directed into the page (The field is zero outside this region). A 5-ohm resistor is connected between points X and Y. The loop is being pulled to the right with a constant velocity of 3 m/s. Make all determinations for the time that the left end of the loop is still in the field, and points X and Y are not in the field.

a. Determine the potential difference between points X and Y.
b. On the figure show the direction of the current induced in the resistor.
c. Determine the force required to keep the loop moving at 3 m/s.
d. Determine the rate at which work must be done to keep the loop moving at 3 m/s.

2. Homework Equations

E = -Blv
V = IR
F = qvB = qE = qV/r
F = P/v
F = BILsin*
I = BAcos*

3. The Attempt at a Solution

a. I said E = -Blv (with E being the emv and potential difference).
So -(.5 T)(2 m)(3/ms) = -3V
Question: Is my length correct? I believe I would use the distance between X and Y if it wants the potential between it...

b. I decided the direction to be counterclockwise (of the current). If the wire loop is being pulled to the right, the area to the right is increasing and the magnetic field to the left is decreasing. If the magnetic field is decreasing to the left, it is increasing to the right. According to Lenz's law, I take the opposite of this to find the current - which would mean counterclockwise direction - and hence the "-" sign in the equation -Blv.

c. I know that F=BILsin* and that I = V/R
So F = B(V/R)L (sin* isn't needed in this equation as the angles are 90)
I also know that E = -Blv (E = emf = V), so:
F = B((-BLv)/R)L, or nicely, -(B^2)(L^2)v/R
Thus, (.5 T)^2 x (4 m)^2 x 3 m/s / 5 ohms = -2.4 N
Question: I have to include the "-" sign in the Blv, right? I would think so since force is a vector and has direction, but I dont know why the force would be negative..

d. The rate at which work is done is power, and P = Fv
So I just multiple my answer in c by 3 m/s.
P = (2.4 N)(3 m/s) = 7.2 W (watts)
Again, I'm not sure of direction. I don't believe you can have "negative" power to the best of my knowledge.

----

Any help is greatly appreciated. I don't necessarily want answers because if I do the work I understand it better, but any direction to my faults would be a big help. Thanks, and have a great day.
 
Actually, as of now.. I'm mostly confused about the signs. I think most of my work is right, so if someone gets a chance, could you maybe help me in that area? If not, that's okay, thanks just for reading this :D
 

Related Threads for: Flux in a Wire Loop w/ a Magnetic Field

Replies
3
Views
24K
  • Posted
Replies
10
Views
3K
  • Posted
Replies
3
Views
6K
Replies
16
Views
895
Replies
1
Views
1K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top