How does a loop of wire in a generator produce alternating current?

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A loop of wire in a generator produces alternating current by rotating in an existing magnetic field, which induces a current according to Faraday's Law. The discussion also highlights that an electric field can generate a magnetic field even without a wire, particularly when the electric field changes over time. Key considerations include the implications of Maxwell's equations and the nature of the electric field in relation to time and space. The conversation emphasizes the relationship between electric and magnetic fields in generating current. Understanding these principles is crucial for grasping the functioning of generators and electromagnetic induction.
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a.by creating current by rotating in an existing magnetic field?
b.by creating a varying magnetic field with its rotational kinetic energy
c.by rotating through areas of high and low electrical force


An electric field produces a magnetic field even when there is no wire to conduct a current provided which of the following is also true?

a.The electric field is between a pair of parallel metal plates.
b.The electric field changes in time but at each instant is the same at every location.
c.The electric field is changing as time passes.
d.The electric field is different from place to place.
e.The electric field does not change as time passes.
 
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It might help if you post some of your thoughts. For the first problem, consider the implications of Faraday's Law. For the second problem, consider Maxwell's extension to Ampere's Law (or Ampere's circuital law as it's named in this link): http://en.wikipedia.org/wiki/Maxwell's_equations

What's happening to the electric field E in this equation?
 
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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