Identical ions, each with charge +e, are situated on twon the opposingte corners of a square with side length L. What is the electric potential caused by these two ions at either of the empty corners of the square?
Question
Identical ions, each with charge +e, are situated on twon the opposingte corners of a square with side length L. What is the electric potential caused by these two ions at either of the empty corners of the square?
Solution
The electric potential V at a point in space due to a point charge q is given by the formula:
V = k*q/r
where:
- k is Coulomb's constant (8.9910^9 Nm^2/C^2),
- q is the charge (in this case +e),
- r is the distance from the point to the charge.
In this case, the distance from either of the empty corners to each of the charges is the length of the side of the square, L.
So the electric potential at either of the empty corners due to one ion is:
V1 = k*e/L
Since the charges are identical and the distances to the point of interest are the same, the potentials due to each charge are the same.
Because electric potential is a scalar quantity, the total electric potential at a point due to multiple charges is simply the sum of the potentials due to each charge.
So the total electric potential at either of the empty corners is:
V_total = V1 + V1 = 2ke/L
This is the electric potential caused by the two ions at either of the empty corners of the square.
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University of MédéaFaculty of Science1st Year MIDepartment of Mathematics and Computer ScienceQuestioning: ElectricityExercise 1:Four point charges are placed at the vertices ABCD of a square with side length ,and center O, the origin of an orthonormal coordinate system (Oxy) with unit vectors and .Given : , , , ,.1. Determine the electric field at the center of the square. Specify the direction,magnitude, and direction of .2. Express the potential created at by the four charges.3. Express the potential on the parts of the axes within the square.Exercise 2:Consider four closed surfaces , and , and three charges , , and . Determinethe electric flux passing through each surface ?D CBA
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