Induced EMF and Current in a Moving Plate Through a Solenoid

[stunner5000pt]

Please help with Induction!

A 0.5m diameter aluminium plate moves downward at 0.1m/s along the axis of a 1m long solenoid proving a magnetic field of 3T at the centre. The plate moves from position 1m above the solenoid and move down to a position 1m below the solenoid. The way it moves is described in the attachment Solenoid.jpg.

First of all is it even possible to find the induced emf in the plate without some really complex (and by complex i mean beyond 2nd year university level) ?? BEcause every question asks for sketch i am guessing that i don't need numbers involved in this

Now onto the quesitons themselves

Sketch a graph of the magnetic field along the path of the plate.

I would guess that the magnetic field is a constant value all along the length of the solenoid and then falls off exponentially at points beyond that

Sketch a graph of the EMF induced in the plate as a function of vertical position
The EMF would be constantly increasing positively as the plate approaches the solenoid from the top, and then while in the solenoid, the emf would be increasing as well and then go to new negative minimum after the plate passed the mid point of the solenoid and then gradually increase?

Sketch how the current flows in the plate.
Eddy currents are the currents within the plate, yes? SO the currents would be circulating parallel to it's circumference?

Sketch a graph of the induced magnetic field from the plate
Not sure but the magnetic field would eventually increase as the induced EMF increased and as a result the induced B would be increasing and then falling off in the same way the solenoids magnetic field fell off?

Sketch a graph of the force on the plate.
F = qvBsin(theta)
SO the force is constantly increasing as the plate moves closer to the solenoid.

Please check my answers i am not sure about some of them. Your help would be greatly appreciated!

 

[vincentchan]

I'll answer your question 1 by 1...

First of all is it even possible to find the induced emf in the plate without some really complex

No, Do I need to explain ?

I would guess that the magnetic field is a constant value all along the length of the solenoid and then falls off exponentially at points beyond that

constant along the solenoid, Good guess...
not quite exponentially, but it indeed falls off really fast, for a ideal magnetic dipole, the field falls off as r^3, but in your case, it is far from ideal, some intense calculation is required to find out how the field strength related to distance.. (find out this relationship has no different with answering your first problem, and I had said no simple solution for you already)

The EMF would be constantly increasing positively as the plate approaches the solenoid from the top, and then while in the solenoid, the emf would be increasing as well and then go to new negative minimum after the plate passed the mid point of the solenoid and then gradually increase?

Increasing: yes, constantly: No, indeed, it increases quite complicated...
if you assume the field is constant along the solenoid, why would the EMF increase as the ring passes its. EMF generates only if there is a CHANGE in magnetic field. Sure, in real life, the field along the solenoid is not constant, however, it is very close, and your assumetion is completely valid.
beware of your direction... is the direction of your EMF same b4 and after passing the mid point. why or why not?

Eddy currents are the currents within the plate, yes? SO the currents would be circulating parallel to it's circumference?

basically, you are right. What about the direction?.. would the current flows Clockwise or CCW? would the direction changes when passing thru the solenoid?

Not sure but the magnetic field would eventually increase as the induced EMF increased and as a result the induced B would be increasing and then falling off in the same way the solenoids magnetic field fell off?

the EMF is proportional to the CHANGE of magnetic field, not the STRENGTH of magnetic field... think..
the field generates by the plate has opposite direction compare with the solenoid, otherwise it will violate the conservation of energy...memorise this, this "rule" works everyway, not only in your case.

F=qvBsin(theta)

completely wrong.
the Force is always opposite to the direction of the motion. as i said before, otherwise it will violate the conservation of energy. One more thing, the larger the EMF, the larger the current, the larger the B field generates by the plate, the larger the force. You can't find a simple formulas for the force, but observe the relationship, and draw the graph should be easy...

 

[stunner5000pt]

i hope the answers i have posted are correct, please tell me if i made any errors

 

[stunner5000pt]

here are the two other ones

In both of these where there is an axis i have taken the right as positive and left and negative the horizontal solid line repsents the midpoint of the solenoid