# Moving Square Loop through a Magnetic Field

## Homework Statement

A square loop of side 1.5m and Resistance 2Ω is pulled with a constant velocity v=0.3m/s through a smaller region with a constant magnetic field B (out of the page) of 4T. The figure shows the position at t=0.

Calculate the magnetic flux of the coil at t=4s..

Here is a picture I made.

http://i.imgur.com/xmyfkVx.jpg

## Homework Equations

E = -dFlux / dt

Magnetic flux = B*Area = B*y*x

## The Attempt at a Solution

Hi,

So I tried solving this and I don't know if I am on the right track or not but I calculated the flux at t=4s. I got 3.6 T*m^2. I did this by flux = B * y*x so
flux = 4T *1.5 (high of the square) * 0.6 (part of the region that is inside the loop)

My question are first, I am not sure if I should be using 1.5 for the high, I kind of feel like i should be using the high of the region which is 0.9 but then again, they are asking for the flux through the COIL, so thats why i used 1.5 (the high). If this is correct, then why am I using 0.6 for the base? Shouldn't i be using 1.5 as well? I am confused this doesn't make any sense any help will be appreciated.

BruceW
Homework Helper
well, in this case, the coil is the loop, right? I think 0.6 for the base is correct, you should use a similar reasoning for the height.

I am very confused now, I thought they were asking for the magentic flux through the area of the coil (loop shown in red) so the area of the coil would be just 1.5^2. If that is the case, then the magentic flux will be that area times the field (4T) but the field is not changing so the flux is constant??? Hence no emf is induced... I have a WTF face right now cause the following questions ask for a graph of current vs T and emf vs T, so it is implied that the flux cannot be constant, The area MUST be changing but I just don't know in what way... :( help please I have a test on Tuesday and I need to understand this

BruceW
Homework Helper
hold on, step back. Generally, the flux through the coil is:
$$\int \vec{B} \cdot d \vec{A}$$
(where A is the area of the coil). And B is not the same over the whole area of the coil.

edit: They tell you where B is zero, and where B is 4T, so you need to use this information to do the integral properly. (In this case, it is a fairly easy integral, because the integrand is zero in some parts, and constant in another part).

wouldn't that integral become B*A since B and the vector dA are parallel? why do you mean by 'They tell you where B is zero, and where B is 4T, so you need to use this information to do the integral properly'

BruceW
Homework Helper
well, in the (smaller) black square, B field = B and outside the black square, the B field = 0
edit: (and yes, they are parallel, so that makes it a bit simpler)

So let me see if I get this right, as soon as some of the magnetic field area gets inside the loop, there is a magnetic flux through the coil, which will be B *A, here the area will be the area from the little square THAT IS INSIDE THE LOOP, so the flux = 4T*y*x
Since height is constant cause the loop is moving horizontally, the only thing that varies with time would be x so, Flux = 4T*0.9*x
at t=4 the loop moved 0.3 m/s *4s or 1.2m so there is 0.6m of the base of the little magentic field area inside the loop. Hence, Flux (at t=4s) = 4T*0.9*0.6.

If I had to graph this Flux vs t, would it look something like this?

http://i.imgur.com/lGwhD75.jpg

Thank you

EDIT: For the graph, the max value is achieved at t=5 until t=7, where the flux starts to decrease.

BruceW
Homework Helper
Yep! That all looks very good. nice work!

Thanks!