Answering General Questions: Electric Field, Potential, Capacitors

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The discussion revolves around clarifying concepts related to electric fields and potentials, specifically addressing whether a zero potential implies a zero electric field, which is clarified as no. It explores the effects of inserting a dielectric into a capacitor, noting that in an isolated capacitor, the energy increases due to increased capacitance, while in a connected capacitor, the energy increases due to a constant voltage. Additionally, it examines the conditions under which the electric field and potential are zero along the line between two equal positive charges, emphasizing the need for detailed explanations of these phenomena. Participants are encouraged to share their reasoning to facilitate understanding and receive assistance. Overall, the thread aims to deepen comprehension of these fundamental physics concepts.
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I'm having trouble answering these questions and i was curious to see how other would answer them:

If the potential at a point is zero, must the electric field also be zero? (No)
Give an example.

How does the energy stored in a capacitor change when a dielectric is inserted if (a) the capacitor is isolated so Q doesn't change, (b) the capacitor remains connected to a battery so V doesn't change.

If there is a point along the line joining two equal positive charges where the electric field is zero? Where the electric potential is zero? Explain.
 
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First you should give your answers with your attempts at the explanation, so that we can understand your thoughts on these. Then you'll get all the help needed.
 

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