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roam
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Homework Statement
A square aluminium loop, of side a and uniform cross-section falls in a vertical plane under gravity, as shown in the diagram. A uniform, horizontal magnetic field B, indicated as the shaded area, points into the page.
(a) If the loop starts when its lower edge is coincident with the lower edge of the magnetic field, how long does it take to clear the field?
(b) We were careful to avoid starting the loop from above the shaded area. Why?
Homework Equations
Attached
The Attempt at a Solution
In the attachment I have already worked out the equation for acceleration, velocity, and terminal velocity.
(a) If I understand correctly, the distance to be traveled in order to clear the magnetic field is ##a## (side length of the square loop).
So since the loop is fully immersed in the magnetic field, it would just accelerate at the local gravitational acceleration g (the flux through the loop would not change if it is fully inside). So
##\frac{dv}{dt} = g - \frac{B^2l^2 v}{mR} = g##
I have used the equation ##s=\frac{1}{2} at^2## to work out the time:
##t=\sqrt{\frac{2s}{a}}=\sqrt{\frac{2(a)}{g}}##
Is this right?
(b) I have no idea. It think the loop would simply start to fall freely with acceleration g, then its acceleration would change when it comes to the upward force exerted by the magnetic field. So why does the question avoid starting the loop from above the shaded area?
Any explanation here would be greatly appreciated.