Voltage around a loop, half inside a capacitor and half outside

In summary, the conversation discusses a problem about the emf in a loop and the solution provided by the author. The author's reasoning is that there is no net emf in any segment of the loop due to the redistribution of charges, while the solution claims that since the integral of the force per charge around the loop is zero, the emf is also zero. There is no contradiction between the two explanations and both seem to be valid.
  • #1
RubinLicht
132
8

Homework Statement


This is not a homework problem, I'm working through griffiths Electrodynamics on my own.
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Homework Equations


upload_2019-2-20_13-25-32.png

when there is an emf source, since electrosatic fields integrate to zero around a loop

The Attempt at a Solution


The solution claims that since the integral of f (force per charge) around the a loop for any electrostatic field is zero, the emf is zero since that is the only field present.

However, when I thought about this problem, I reasoned that initially the charges in the wire would rapidly reorient themselves to cancel out the external field. and since the field is 0 through out the wire, and there isn't a source of emf that generates potential differences in the metal, the current is naturally zero. This is very different reasoning, and i don't think the solutions are valid. Can anyone confirm/deny please?
 

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  • #2
The problem asks about "the emf in the loop". It's unclear what that means.
The reasoning offered explains why there should be no net emf in one complete trip around the loop, hence no sustained current. Your reasoning is that once the initial redistribution of charge settles down there is no net emf in any segment of the loop.
I see no contradiction, and both appear valid.
 
  • #3
There is no source of emf anywhere within the loop so the current is obviously zero. Seems like what you reason and what the author reasons is the same. No emf!
 

Related to Voltage around a loop, half inside a capacitor and half outside

1. What is the relationship between voltage and a loop?

Voltage is a measure of the electric potential difference between two points in a circuit. In a closed loop, the total change in voltage around the loop must be equal to zero, as energy cannot be created or destroyed. This is known as Kirchhoff's Voltage Law.

2. How is voltage distributed between a capacitor and the rest of the loop?

When a capacitor is placed in a circuit, it stores electrical energy in the form of an electric field. Half of the total voltage around the loop will be across the capacitor, and the other half will be distributed among the other components in the loop.

3. Why is half of the voltage outside of a capacitor?

A capacitor is essentially two conductive plates separated by an insulating material. When a voltage is applied to the capacitor, one of the plates becomes positively charged and the other becomes negatively charged. This creates an electric field between the plates, resulting in half of the total voltage being stored outside of the capacitor.

4. How does the voltage change when a capacitor is added to a loop?

The addition of a capacitor to a loop will change the distribution of voltage in the circuit. As mentioned before, half of the voltage will be across the capacitor, while the other half will be distributed among the other components in the loop. This can affect the overall voltage and current in the circuit.

5. Is the voltage the same across all points in a loop?

In an ideal circuit, the voltage should be the same at all points in a loop. This is due to the conservation of energy and Kirchhoff's Voltage Law. However, in real-life circuits, there may be some variation in voltage due to factors such as resistance and capacitance.

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