Faraday's Law of Induction: Why is EMF Inversely Proportional to Time?

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Faraday's law of induction states that the electromotive force (EMF) is directly proportional to the number of turns in a coil and the magnetic field strength, while being inversely proportional to time. The inverse relationship with time indicates that a faster change in the magnetic field induces a greater EMF. If the magnetic field remains constant over time, no induced EMF occurs, highlighting the necessity of change for induction. The discussion emphasizes the importance of understanding the dynamics of changing magnetic fields in relation to EMF. Clarifying these concepts is essential for grasping the principles of Faraday's law.
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Hi, I am doing coursework on Faraday's law of induction. My assignment was to carry out experiments which confirm Faraday's law and also to explain the physics of how faraday's law works... My experiments all worked perfectly, producing straight line graphs showing that:
\epsilon\propto N
\epsilon\propto B
\epsilon\propto\frac{1}{t}

I did not do any experiments to test \epsilon\proptoA ...

I have explained the physics behind the first two results, but for the life of me I can't justify WHY the EMF is inversely proportional to time... I have thought about F = BIl = \frac{BQl}{t}, therefore the force on the delocalised electrons is inversely proportional to time... But it's all dead ends after that...

Any help would be GREATLY appreciated!

Thank you in advance!
 
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Well if your EMF didn't vary with time, it would mean that your magnetic field would remain constant. Without it changing you cannot get an induced emf (well something has to change with time essentially).
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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