Metal Magnetic Flux 9: Calculate Induced Current & Resistance

[dangish]

9. Two sliding metal bars of length l = 15.0 cm are moving along two parallel rails, in
opposite directions, with constant speeds of v = 0.7 m/s, as shown in the figure below.
The rails are located in a uniform magnetic field with a magnitude 0.35 T that is directed
into the page as shown.

(a) Calculate the rate of change of magnetic flux within the loop formed by the sliders
and the rails.

(b) In what direction does the induced current flow around the loop? Indicate this clearly
on the diagram and briefly justify your answer.

(c) If that current is 0.25 A, calculate the total resistance of the loop.

The picture is in the attachment if you need it.

I have an exam on monday, I am not very good at this stuff, the professors not giving solutions and I can't figure this one out.

only equation I found that was relevant is,

Integral of B.ds = u0I + u0e0 x(dfluxe/dt)

and integral of E.ds = -dfluxb/dt

Can someone please help me!

 

[Rick88]

To solve the problem you need to useFaraday's law of induction

In particular, \frac{d\Phi}{dt} = \epsilon = Bvl (This formula is in the "Direct evaluation of the change in flux" paragraph).
Substitute and you have your answer for a).

Part b) is just some basic knowledge of the direction of B knowing the direction of velocity and current.

For part c) you can use your \epsilon found in a) as Voltage (\epsilon stands for electromotive force, which is basically equivalent to voltage) and find R using Ohm's Law.R.

 

[dangish]

so that e is the rate of change of magnetic flux? what are the units for that? something per second I would imagine.

 

[dangish]

actually I guess the units are Tesla/s

And for part b you can just change that to voltage?

 

[dangish]

also, since there are two velocities, -0.7 and +0.7 m/s

which one should I use?

 

[Rick88]

\epsilon is just a voltage, so it's measure in Volts.

How about using a summation with v=1.4ms-1 and then v=-1.4ms-1?

 

[dangish]

I vaguely understand what you mean by summation there

 

[dangish]

LaTeX Code: \\epsilon = (.35T)(.7m/s)(.15m) = .0368T/s is what I did for part a.)

 

[Rick88]

I vaguely understand what you mean by summation there

Ok, let's think about the process itself.
The change in magnetic flux is proportional to the area swept by each bar.
In 1 second, the bar traveling to the right would have swept Acm^2.
During the same time, bar traveling to the left would have swept how much?

 

[dangish]

It would have swept the exact same amount of area?

 

[dangish]

-Acm^2

 

[Rick88]

Areas are not vectors. So just A cm^2, right?

 

[dangish]

fair enough, where does this lead us exactly? I still don't know what to use for the velocity

 

[Rick88]

You should have two terms.
One for +0.7ms-1, one for -0.7ms-1, but you can neglect the minus of the latter.

 

[dangish]

so would I have to use the same equation twice?
or are you saying I can just use e=(.35T)(.7m/s)(.15m)

 

[Rick88]

you have to use it twice.

 

[dangish]

e1=(.35T)(.7m/s)(.15m) = .0368T/s

e2=(.35T?(.7m/s)(.15m)=.0368T/s

etot= e1+e2 = .0368T/s + .0368T/s = .0736T/s

is this correct?

 

[Rick88]

I believe so.

 

[dangish]

thank you good sir, patience is a virtue, especially when dealing with me.

Cheers!

 

[Rick88]

You're welcome.

R.