Total induced emf at different speeds

AI Thread Summary
The discussion centers on the relationship between the speed of a coil moving towards a magnet and the total induced electromotive force (emf). According to Faraday's law, the induced emf is related to the rate of change of magnetic flux over time. When the coil is moved faster, the instantaneous induced emf increases due to a higher rate of change of magnetic flux. However, the total time of movement decreases, which complicates the relationship between speed and total induced emf. Ultimately, the total induced emf may differ depending on the speed of the coil's movement.
cryptoguy
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Homework Statement


Suppose you have a coil that is a certain distance from a magnet. Now you move the coil towards the magnet (until it is on top of the magnet) at a certain speed. Then you do the same thing only faster. Will the total induced emf be the same for both tries? Aka should the integrals of the two V_induced vs t plots be the same magnitude, opposite sign?


Homework Equations


Faraday's...


The Attempt at a Solution


I'm not at all sure... I'm doing a lab on this and be got different values for the total induced emf, but I have a hunch that it should be the same, can't really explain it though.
Thanks for any hints.
 
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Faraday's law basically states that the induced emf is equal to the rate of change of the magnetic flux with respect to time. Now, if you move the magnetic through the coil faster, does the rate of change of magnetic flux with respect to time remain unchanged, increase or decrease?
 
if you move it faster... sounds like it'll increase
 
cryptoguy said:
if you move it faster... sounds like it'll increase
Correct! So what would happen to the induced emf?
 
it would... also increase? Yet if you move the coil faster towards the magnet, the instantaneous induced emf does increase, but the total time of movement decreases.
 
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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