Electric Potential in electric fields true/false

[physninj]

Homework Statement

1. If the electric field is zero at a point, the potential must also be zero at that point

2. If the electric potential is zero in some region of space, then the electric field must also be zero in that region.

3. If the electric field is zero in some region of space, then the electric potential must also be zero in that region.

4. Electric field lines point towards regions of lower potential

5. the value of electric potential can be chosen to be zero at any convenient point in spave

6. The capacitance of a conductor is defined to be the total amount of charge it can hold.

7. The capacitance of a parallel-plate capacitor depends on the voltage difference between
the plates.

8. The equivalent capacitance of two capacitors in series is less than that of either
capacitor.

9. Since V is energy per unit charge, the total energy in a capacitor is QV.

10. Electrostatic energy can exist in space even if there are no charges or mass in that space.

The Attempt at a Solution

1. F because if the point is perfectly between two E-fields potential is doubled

2. ? I don't understand when they start talking about regions of space

3. ?

4. T
5. T
6. F
7. F
8. T
9. T
10. T

Numbers 2 and 3 are where I feel like I'm at a loss. If you disagree with the rest then I may need help there too but I'm reasonably confident. Thank you for any help :)

 

[Simon Bridge]

1. F because if the point is perfectly between two E-fields potential is doubled

What is the relationship between electric field and electric potential?
How is electric potential measured?

2. ? I don't understand when they start talking about regions of space

Do you not know what "region of space" means? Try "volume of space".

Imagine a wire that has length 1m and electric potential is +P on one end and -P on the other, then at east one point on the line must be zero right? So you investigate and, instead of one point, there is a whole 10cm in the middle of the line where the potential measures zero. Is the electric field in there also zero?

#3 is the reverse of this.
All the places you get stuck seem to be asking about the relationship between the electric potential and the electric field. So focus on that.

I didn't check the others.

 

[physninj]

That first answer came straight out of my understanding of the textbook so if that is wrong for some reason then I am back at square one. I'm sorry but I'm frustrated, I don't understand how my nose can be in my textbook and still not be able to figure these problems out.

Why would there be a whole ten cm where the potential is zero? If that case were true I would say that there is still an electric field in the ten cm region, rendering the answer false. but how I'm supposed to make sense of your hint other then that I don't know. Maybe I'm not that smart, sorry.

Thanks for your guidance. Number 5 also seems a little flimsy but was also taken from a statement in the textbook. Says you can take potential to be zero anywhere in space that's convenient, it seems to conflict with the answers I'm trying to get to for 1-3.

I'm seeing now that the electric field is the gradient of the potential? I'm still having trouble putting the pieces together though.

 

[ehild]

Both the electric field and the potential are functions of position. The electric field is the negative gradient of potential. In one dimension,E(x) it is the negative slope of the potential U(x): E(x)=-dU/dx; it points towards decreasing potential. If the potential is constant in a region (say from x=0 to 1m) the slope of U(x) is zero.
Imagine a hollow metal sphere. You give some charge to it. There is electric field around it, but inside the sphere, the field is zero. Outside the sphere, the potential decreases with the distance from the centre of the sphere. Inside the sphere, the potential is constant.

Your answer to question 9 is wrong.

ehild

 

[physninj]

Your answer to question 9 is wrong.

ehild

Good catch, I appreciate that. It's potential energy per unit charge, and even that applies to a test charge not a capacitor if I'm understanding correctly.

So using my new understanding of the E-field being the slope pointing towards lower potential I have:

1. F if the electric field is zero, the electric potential must be CONSTANT, not necessarily zero

2. T if potential is zero over a region, it is therefore constant over that region and the slope (E-field) must be zero.

3. F. If the electric field is zero at a point, the potential may be at a maximum or minimum at that point, not necessarily being zero. :)


5. I'm still not positive on, I'm thinking false now because in some cases in space there has to be a potential. Quote from my textbook that lead me to believe this to be true:


"There's nothing particularly special about the place where potential is zero; we can define this place to be wherever we want it to be."

You can see how that just confuses the heck out of me if #5 is false. Thanks Ehild.

 

[ehild]

#5 is true. The potential is integral of the electric field: the integration involves an arbitrary constant. It depends where you want the potential to be zero.
In case of a point charge, it is convenient to choose the constant that the potential is zero in infinity. So the potential of a charge Q is kQ/r.

ehild

 

[Simon Bridge]

I was going to say... potential is measured by comparing the potential at one place with that at another place.
By default, we set the reference potential at infinity. Sometimes that is not convenient, and we pick another place; like the ground, or the negative terminal of a battery, or the black probe on a voltmeter.

Thus a zero potential someplace just means that the potential there is the same as the reference potential.

When the book says we can put the zero-potential anywhere we like, it is saying we can put the black probe of the voltmeter anywhere.