Show that the potential at a generic point for x positive is zero

In summary, the potential at a point (-x, 0, 0) is zero when two point charges of equal magnitude but opposite signs are placed at (-a, 0, +a) and (-a, 0, -a) and their corresponding mirror charges are placed at (a, 0, +a) and (a, 0, -a). This is because the voltage formula, when calculated, results in a value of zero due to the opposite charges cancelling each other out.
  • #1
blueyellow

Homework Statement



Show that in this set-up, the potential at a generic point (-x, 0, 0) (for x positive) is zero:

two point charges placed at (-a, 0, +a) and (-a, 0, -a)
the mirror charges are (a, 0, +a) and (a, 0, -a)

The Attempt at a Solution



V=(q/(4 pi epsilon0)) ((1/(sqrt((x^2 -a^2)+a^2))+(1/(sqrt((x^2 -a^2)+a^2)))

this does not equal zero

by the way, please DO NOT DELETE THIS POST, MODS, I ASSURE YOU I HAVE NOT POSTED THE SAME QUESTION. IT IS A TOTALLY DIFFERENT PART OF A QUESTION I POSTED EARLIER.
 
Physics news on Phys.org
  • #2
Yeah, you're right, the voltage is not zero. That's weird. Are you sure the charges are supposed to be the same? Opposite charges at those locations would give V = 0.
 
  • #3
thanks, sorry, i wasn't paying attention to the part of the question that said 'two point charges +q and -q'
 

1. What does it mean to show that the potential at a generic point for x positive is zero?

Showing that the potential at a generic point for x positive is zero means proving that the electric potential at any point along the x-axis, where x is a positive value, is equal to zero. This indicates that there is no electric field or charge present at that point.

2. How is this potential calculated?

The electric potential at a point is calculated by taking the ratio of the work done by an external force to move a unit positive charge from infinity to that point. Mathematically, it is represented as V = W/q, where V is the potential, W is the work done, and q is the charge.

3. Why is it important to show that the potential is zero at a generic point for x positive?

Showing that the potential is zero at a generic point for x positive is important because it helps us understand the behavior of electric fields in that region. It also helps in solving various electrical engineering problems and predicting the movement of charges in the presence of an electric field.

4. Can the potential at a generic point for x positive ever be non-zero?

Yes, the potential at a generic point for x positive can be non-zero if there is a charge or an electric field present in that region. In such cases, the potential will be influenced by the presence of these factors and will not be equal to zero.

5. How does this potential relate to electric potential energy?

The electric potential at a point is directly proportional to the electric potential energy of a charge placed at that point. This means that as the potential increases, the potential energy of the charge also increases. Additionally, the electric potential energy can also be calculated using the formula U = qV, where U is the potential energy, q is the charge, and V is the potential.

Similar threads

  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
525
  • Introductory Physics Homework Help
Replies
1
Views
875
  • Introductory Physics Homework Help
Replies
6
Views
140
  • Introductory Physics Homework Help
Replies
23
Views
337
  • Introductory Physics Homework Help
Replies
3
Views
543
  • Introductory Physics Homework Help
Replies
16
Views
389
Replies
22
Views
1K
  • Introductory Physics Homework Help
2
Replies
64
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
2K
Back
Top