Is Electrostatic Potential Zero When Electric Field Is Zero?

[burak_ilhan]

1}If the electric field is zero in some region, must the potential also be zero?An example?

2}Give an example of a conductor that is not an equipotential.Is this conductor in electrostatic equilibrium?

3)If a high voltage cable falls on top of your automobile, will you probably be safest if you remain inside the automobile.Why?

4)If we surroun some region with a conducting surface, we shield it from external electric fields. Why can we not shield a region gravitational field by a similar method?

Its clear that these questions need no mathematical work,i'd like to discuss them with forum members

 

[Palpatine]

You gave the answer to 3 in 4.

 

[burak_ilhan]

yes but a car is not compeletely closed with metal(windows).And what will happen if you open a door and try to get out?

 

[cookiemonster]

1) No, it just means that the potential isn't changing. Remember that potential is a totally relative quantity, anyway. You can define the potential relative to 0V or relative to 50,000,000V if it floats your boat.

2) Here's half of it: a conductor in an electrostatic arrangement will also be equipotential. There was actually a nice little discussion about it in a different thread, https://www.physicsforums.com/showthread.php?s=&threadid=15931&perpage=15&pagenumber=1

3) Oh yes. If that does happen, don't get out and don't touch the ground! Remember that your car is insulated from the ground by your tires (unless your exhaust or something is dragging , like my poor car is apt to do), so it's just going to hold all that charge. If you, a pretty nice conductor, decide to try to step out of the car, you're going to be a path for that charge the car is holding to travel through to the ground. I don't know about you, but I'd rather not be a make-shift powerline.

4) There's no negative mass like there is negative charge.

cookiemonster

 

[Palpatine]

The car is not insulated from the ground by the tires because the electric field of the lightning bolt is strong enough to cause the air surrounding the car to undergo electrical breakdown. In other words the charge gets conducted through the air to the ground.

 

[burak_ilhan]

the absence of electrostatic fields in closed conducting cavities is proved by using the idea that the electrostatic field as a conservative field:

0=\oint E.dl

this equation implies that a field line can never form a closed loop.
In my opinion this cannot be applied to gravitational fields because gravitational field lines can form a closed loop.Is that correct?If it is anyone knows how to explain this mathematically?

 

[kuengb]

In my opinion this cannot be applied to gravitational fields because gravitational field lines can form a closed loop.Is that correct?If it is anyone knows how to explain this mathematically?

They can't. The line integral formula you wrote down means that a field is conservative, as you said. Well a grav. field definitely is!

My response to 2:
A conductor that is not in equipotential "contains" an el. field, the result is a current, so it isn't an electrostatic situation. An example for this is the cable that sends the signal to your screen right now. But as long as we have electrostatic equilibrium in a conductor, we have an equipotential.