Potential of 0 Question

[betterfuture]

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I've been trying to get this last part of potential down before I can complete the whole picture. Okay.

So Potential is just the amount of work it takes to move a charge from infinity to space. And in that space there is a source charge that sets up an electric field. Now depending on the charge that you move, the amount of work required to move that charge will differ.

So question is, when will there be a potential of 0. I know if there is no electric field then the V is 0. But I am trying to think when it would be 0 if there was an electric field set up?

 

[wizzed101]

The convention is that +J denotes the amount of energy supplied to the system and -J the amount of energy spent by the system.

Electrical Potential has the unit of J and is the amount of work "happens" when a charge moves from a position to infinity.

If the two charges in question are of the same nature, U will be positive which means the system gains energy when one is moved. This should be intuitive. On the other hand, if two charges are of opposite signs, then the system must expend energy to separate them so U will be negative.

It is obvious that when U is near 0, the energy gained or spent must be negligible. And that happens when the two charges are far way from each other.

 

[betterfuture]

So let's give an example. Say a source charge is +4Q and sets up an electric field and a test charge, -2q, comes along. Naturally, they would attract, lowering their potential energy. So where would the potential be 0 in this case?

Also, does doing work mean moving a certain way in the electric field? Like if a source charge has radiating lines that set up an electric field, work would only occur to move a test charge if you move perpendicular to the field lines. Is there a use of sin/cos involved?

 

[wizzed101]

You don't understand the concept of electrical potential. Read my post above again. You can have two fixed charges in space and they will still have an electrical potential.

"Naturally, they would attract, lowering their potential energy."

No. The potential energy is the same. Now let say they did move, then the potential energy decreases in the sense that its numerical value gets more negative (and its absolute value increases).

"does doing work mean moving a certain way in the electric field?"

As long as it doesn't move along the field line, there will be a none zero work involved. And yes, there will be sin and cosine, just like in traditional work calculations.

What is "field" anyway?

 

[theonlytycrane]

Not sure if this will help, but here are two examples to consider:

Case 1: An E-field is setup by a source charge +q. A test-charge of +q is placed in the E-field and will accelerate away. Potential energy U = k * q * q / r, which decreases as r increases (+q moving farther away).

Case 2: The same E-field as Case 1 except the test-charge is -q meaning that the test charge will accelerate toward the source charge. Potential energy U = -k * q * q / r, which decreases (gets more negative) as r decreases.

The test-charge always moves down it's potential energy gradient, but specifics can depend on the sign of the source and test charges.

 

[betterfuture]

There was a question I had.

The charges, +Q and -2Q, are fixed at a distance d to the left and d to the right of the origin along the x-axis. The potential indefinitely far from charges is equal to zero. Find the position on the x-axis CLOSEST TO THE ORIGIN where the potential is also zero.

a) d/3 to the left if the origin
b) 2d/3 to the left of the origin
c) d/3 to the right of the origin
d) 2d/3 to the right of the origin

 

[wizzed101]

That is a nonsensical question.

 

[betterfuture]

Lol why?

 

[wizzed101]

By definition, electrical potential energy is the energy that is spent (-) or gained (+) to move a charge from its current position to infinity. The question basically asks you to find a place between those 2 charges such that you can move some random charge at said position to infinity without spending or gaining energy.

 

[wizzed101]

BUT since this is a test and you can't sue the creator. The "solution" probably goes like this:

-2qk/r1 + qk/r2 = 0
r1 + r2 = 2d

solve that the first eqn:

2/r1 = 1/r2 --> r1 = 2 r2

solve the second equation:
3r2 = 2d -> r2 = 2/3d

Since I set r2 as the distance from the charge +Q which is on the left, the answer is a)

 

[betterfuture]

Stuff like this is the reason why I despise physics. But thank you!

 

[BerkReviewTeach]

Electrical Potential has the unit of J and is the amount of work "happens" when a charge moves from a position to infinity.

Electrical potential is NOT the same thing as work or potential energy (otherwise they would call it the same thing)! It does NOT have units of J! It has units of Volts. What you have posted is a common error many people make, which is likely a big part of much of the misunderstanding. A volt is a J/C, which means that electrical potential is PE/q. It is similar to PE, but not the same.

That is a nonsensical question.

Lol why?

It could be a pretty good question if it had a correct answer. It has potential to be a good question. What they were trying to ask is a typical question in many physics classes.

What would have made this question better, besides actually having a correct answer choice, is to consider the concept of potential. We teach our students to think of potential as "potential to move". If you have no net force acting on you, then you have no potential to move. In the question, you need to determine where a test charge could be placed in that system to have zero potential to move (i.e., feel no net force). It would only be possible to the have zero potential if you were to the left of both charges making up the field, in such a way that the distances are in a root2 : 1 ratio.

 

[betterfuture]

Electrical potential is NOT the same thing as work or potential energy (otherwise they would call it the same thing)! It does NOT have units of J! It has units of Volts. What you have posted is a common error many people make, which is likely a big part of much of the misunderstanding. A volt is a J/C, which means that electrical potential is PE/q. It is similar to PE, but not the same.



It could be a pretty good question if it had a correct answer. It has potential to be a good question. What they were trying to ask is a typical question in many physics classes.

What would have made this question better, besides actually having a correct answer choice, is to consider the concept of potential. We teach our students to think of potential as "potential to move". If you have no net force acting on you, then you have no potential to move. In the question, you need to determine where a test charge could be placed in that system to have zero potential to move (i.e., feel no net force). It would only be possible to the have zero potential if you were to the left of both charges making up the field, in such a way that the distances are in a root2 : 1 ratio.

Always here to save the day! Thank you for the detailed input. Gotta go over this stuff a little more!

 

[wizzed101]

Electrical potential is NOT the same thing as work or potential energy (otherwise they would call it the same thing)! It does NOT have units of J! It has units of Volts. What you have posted is a common error many people make, which is likely a big part of much of the misunderstanding. A volt is a J/C, which means that electrical potential is PE/q. It is similar to PE, but not the same.

Tbh, I assumed that he was talking about the one with "J" because he mentioned work. Even in his question, I can use either concept to arrive at the same numerical answer. I don't even know what is the use of the former except for as a basis to conceptualize the latter.

"Potential to move" doesn't match the formal definition though.

 

[BerkReviewTeach]

"Potential to move" doesn't match the formal definition though.

But it works really well for the MCAT. Consider a point of Zero potential energy, equating to a potential of 0/q = 0. That point would have Zero potential in addition to Zero potential energy. An object with zero potential energy when released will not move. So while it is not the definition, it is a very good way to think about the concept at the level of MCAT questions. For a circuit, the cathode has high potential and the anode has 0 potential, meaning the current will leave the cathode at full potential and stop at the anode. This fits the formal definition and BR's simplified perspective quite nicely. Our teaching philosophy is to go in depth where needed, but simplify where students traditionally struggle. Our students would get pummeled in graduate level physics classes, but they do quite well on MCAT physics with this approach.