Electric potential due to two point charges

In summary, the problem involves finding the electric potential at point P, which is a distance z above two point charges a distance d apart. The formula used is V = Kq/r, and the total potential is found by adding the potentials of the two charges. However, this does not give the correct answer as it implies a zero electric field, which is not always the case. The correct approach is to calculate the derivative of V with respect to z at point P, and use the known electric field of a point charge to find the other components of the total electric field at point P.
  • #1
aftershock
110
0

Homework Statement



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Two point charges (opposite signs, equal in magnitude) are a distance d apart. Point P is a distance z above both charges and horizontally equidistant. Find the electric potential at point P.

Homework Equations



Kq/r


The Attempt at a Solution



It's my understanding that direction does not matter with potential so r is the same value for both. We can add the potentials together to get total potential. Plugging in q for the first charge and -q for the second gives 0.

I know that's not right, that would imply the electric field is zero which is obviously incorrect.

What am I doing wrong?
 
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  • #2
What's your reason for saying that zero potential implies zero electric field?
 
  • #3
TSny said:
What's your reason for saying that zero potential implies zero electric field?

E = -∇V

gradient of zero is zero
 
  • #4
Not necessarily. For example, sin(x) = 0 at x = 0. But the derivative of sin(x) is not zero at x = 0. Likewise, if the potential happens to be zero at some point, it doesn't mean that E has to be zero at that point.

But, if V = 0 (or any other constant) throughout some region of space, then E would be zero in that region.
 
  • #5
TSny said:
Not necessarily. For example, sin(x) = 0 at x = 0. But the derivative of sin(x) is not zero at x = 0. Likewise, if the potential happens to be zero at some point, it doesn't mean that E has to be zero at that point.

But, if V = 0 (or any other constant) throughout some region of space, then E would be zero in that region.
Yeah, what I mean was that it would imply zero electric field only at point P. Is that incorrect?

EDIT: Never mind I just read the "if the potential happens to be zero at some point, it doesn't mean that E has to be zero at that point."So does that mean that zero potential is correct?
 
  • #6
aftershock said:
Yeah, what I mean was that it would imply zero electric field only at point P. Is that incorrect?

No. Suppose V as a function of position (x, y, z) happens to be V = -x - y2 + 2z. Then note that V = 0 at (x,y,z) = (1, 1, 1). What would E be at that point?
 
  • #7
aftershock said:
So does that mean that zero potential is correct?

Yes.
 
  • #8
TSny said:
Yes.

I really appreciate your help but I'm a little confused.

The problem states "Compute E = -∇V , and compare your answer with Prob. 2.2a"

2.2a is the same problem but instead asks to calculate the electric field.I understand now (thanks to you) why I can't simply differentiate the value of potential at some specific point, but then how do I go about this problem?
 
Last edited:
  • #9
Good question. You can see that V = 0 as long as you stay on the z axis. So, if you are at point P and move up or down along the z axis, V remains constant. So you should be able to deduce what the derivative of V is with respect to z at point P. That will give you one of the components of the electric field.

To get the other components you need the derivative of V with respect to x and y at point P. This would require knowing how V varies as a function of x and y as you move parallel to the x and y axes from point P. Your calculation of V at point P does not give you that information. So, the question seems to me to be a bad question unless the question is just to get you to see that the one component of E that you can calculate is consistent with what you found for that component in the other problem.
 
  • #10
You should already know the electric field of a point charge. Just like you can add potentials, you can add fields. The total field is the sum of all the fields of the point charges. Remember, the electric field is a vector, with components in the x, y, and z directions. TSny has already explained that the z component of the electric field will be 0, but you don't necessarily need that when using the superposition method.
 

1. What is the formula for calculating the electric potential due to two point charges?

The formula for calculating the electric potential due to two point charges is V=k(q1/r1 + q2/r2), where k is the Coulomb's constant, q1 and q2 are the charges of the two point charges, and r1 and r2 are the distances from the two point charges to the point where the electric potential is being calculated.

2. How does the distance between two point charges affect the electric potential?

The electric potential is directly proportional to the distance between two point charges. This means that as the distance between the two point charges increases, the electric potential decreases, and vice versa.

3. Can the electric potential due to two point charges be negative?

Yes, the electric potential can be negative if the two point charges have opposite signs. This indicates that the electric potential energy is decreasing as the charges move closer together.

4. What is the unit of electric potential?

The unit of electric potential is volts (V) or joules per coulomb (J/C). This represents the amount of work needed to move a unit of electric charge from one point to another against the electric field.

5. How does the angle between two point charges affect the electric potential?

The angle between two point charges does not affect the electric potential. The electric potential is only dependent on the distance between the two point charges and not the direction in which they are placed.

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