Solving a Physics Problem Involving a Square & Magnetic Field

AI Thread Summary
The physics problem involves a square moving out of a magnetic field, where the induced EMF causes a clockwise current due to a decrease in magnetic flux. As the square exits the field, the induced magnetic field opposes the motion, raising questions about the forces at play. The discussion highlights the need to calculate the current in relation to the square's position and velocity, particularly before and after it reaches a specific point in the field. The user is trying to determine the relationship between current, power, and the variables involved in moving the square out of the magnetic field. Understanding these dynamics is crucial for solving the problem effectively.
Frillth
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Homework Statement



I have the following problem for physics homework:

mkakra.png


We are supposed to take t=0 as the instant when the corner of the square is just about to leave the magnetic field.

Homework Equations



Unsure.

The Attempt at a Solution



Since the magnetic flux will decrease as the square leaves the field, the induced magnetic field because of the induced EMF in the square will also point downward. This tells us that the current will flow clockwise.

That's all I've got so far, and I don't even know if it's right. What is producing the forces here that would oppose our push on the square?

Edit: OK, I think that before tv=L/sqrt(2), power is 2IBtv^2. After tv = L/sqrt(2), power is 2IBv(sqrt(2)L - tv). Is it true that the current in the wire will change as the square gets pushed? If so, what do I do to figure out what current is in terms of the other variables?
 
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How much power is needed to move the loop outside the B-field?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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