HW question: electricity and magnetism

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In a region where electric potential is constant, the electric field must be zero throughout that region. This is because a constant potential indicates no change in potential energy, which corresponds to no electric field acting on a charge. The confusion arises from the possibility of having zero or nonzero electric fields in other contexts, but in this specific case, the correct understanding is that the electric field cannot be nonzero if the potential is constant. The discussion highlights the importance of understanding the relationship between electric potential and electric field strength. Clarification on this concept is essential for solving related problems accurately.
matt85
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The potential is constant throughout a given region of space. Which of the following statements is true? Be sure you can justify your answer.

1. The electric field is zero in this region.
2. The electric field may have places where it is zero, and places where it is nonzero in this region.
3. The electric field is nonzero in this region.
4. The electric field may be zero or nonzero everywhere in this region.

I thought it would be #2, but it was wrong, so could someone please help me out?

Appreciate any help greatly,
Matt
 
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Which potential is constant? Electric, magnetic, gravitational, etc.?

If the Electric potential, then V = integ(E dot dL), so E would have to be zero.


Edit -- Oops, I forgot we weren't supposed to give answers in the HW forum. My bad. Hope I'm right!
 
It is electric potential, but I don't understand why the electrical field would be zero. I was thinking maybe it could be zero or nonzero everywhere?
 
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