Find induced current, magnetic force, work in inclined plane

AI Thread Summary
The discussion focuses on calculating induced current, magnetic force, terminal velocity, and work done by gravity on a conducting bar sliding down inclined rails in a magnetic field. The current is determined using the formula I = emf/R, with adjustments for the angle of inclination affecting the magnetic force calculation. The magnetic force is expressed as F = IBL, with the current needing to account for the angle to ensure it is perpendicular to the magnetic field. The relationship between gravity and magnetic force at terminal velocity is also explored, emphasizing the need to find the correct velocity formula. The conversation concludes with a suggestion to refer to a video resource for further clarification on the concepts discussed.
Helly123
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Homework Statement


http://[url=https://ibb.co/b3Emfo]https://preview.ibb.co/gLaEY8/20180527_055248.jpg[ [ATTACH=full]226218[/ATTACH] A conducting bar slides down without friction on a pair of conducting rails separated by distance d. Connected to resistor R and there magnetic field B directed upward, perpendicular to the ground over the entire region through which the bar moves.
1) find the current
2) find the formula for magnetic force
3) After sufficient of time bar moves at constant speed. At this terminal velocity u the gravity force is balanced by the magnetic force along the inclined plane
Find correct formula for u?
4) what is the formula for rate of work done by gravity on the bar?

[h2]Homework Equations[/h2]
I = emf/R
I = (vBLsin ##\theta## )/R

[h2]The Attempt at a Solution[/h2]
1) current
I = emf/R
I = (vBLsin ##\theta## )/R
I = ( v cos ##\theta## B L sin 90)/R

Is B perpendicular to ground? Not to the inclined plane?
So we need v cos theta which perpendicular to B, and makes sin theta to sin 90 ?

2) Find formula for magnetic force
F = IBL sin 90
The answer is (v##d^2B^2 cos^2\theta##)/R
Why ##cos^2\theta##? Because
The current in 1) after calculation with v cos ##\theta## is perpendicular to B that is I cos ##\theta## ?

3)
Could it be gravity forced balanced by F sin ##\theta## ?
Do we have to find u = velocity?
If yes. How is velocity and force related?

4)
W = mg
##\Sigma##F = m.a
 

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Please post the questions related to the problem statement separately from your attempt at a solution . It is difficult to separate what these are from the questions you have about how to solve the problem. Thank you.
 
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kuruman said:
Please post the questions related to the problem statement separately from your attempt at a solution . It is difficult to separate what these are from the questions you have about how to solve the problem. Thank you.
Ok sir
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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