TA: Calculating Induced EMF in a Square Loop with a Uniform Magnetic Field

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To calculate the induced electromotive force (emf) in a square loop of wire with each side measuring 20 cm in a uniform magnetic field directed into the page, one must apply Faraday's law of induction. The induced emf is determined by the rate of change of magnetic flux through the loop, which is calculated using the formula V_induced = dφ/dt, where φ is the magnetic flux. The area of the square loop is essential for this calculation, and the problem requires information on the magnitude of the magnetic field and how it changes over time or the motion of the loop. Understanding Lenz's Law is also crucial, as it explains the direction of the induced current generated in the loop. To generate a current, either the magnetic field must change or the loop must move in relation to the field.
Giuseppe
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Hey, I'm in a high school AP class and am stuck! Can anyone help me with this problem concerning induced emf? I would surely appreciate it.

There is a loop of wire, shaped like a square. Each side is 20 cm long.
There is a magnetic field directed into the page.

What would be the way of finding out what the induced emf in the loop. The back of the book says that the answer is 1.40 x 10^-4 Volts.
 
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Well, how is an induced current 'created'. I mean, what will you need to do, so that a current is generated in the loop ? What will have to change ?

regards
marlon

ps : LENZ'S LAW (or more generally, the Faraday induction law)is the direction you are looking for.
 
Giuseppe said:
Hey, I'm in a high school AP class and am stuck! Can anyone help me with this problem concerning induced emf? I would surely appreciate it.

There is a loop of wire, shaped like a square. Each side is 20 cm long.
There is a magnetic field directed into the page.

What would be the way of finding out what the induced emf in the loop. The back of the book says that the answer is 1.40 x 10^-4 Volts.
You are missing some important information such as the magnitude of the field and either its rate of change or the motion of the loop.

The induced emf is given by Faraday's law:

V_{induced} = \frac{d\phi}{dt}

In this case, the flux is BA where A is the area of the square loop. How does this change with time?

AM
 
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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