1. For three given electric charges (see the diagram below), calculate the total electric potential in points A and B using the superposition princi- ple. Give the answer in terms of Q and R, for ke = 1 a.u. (arbitrary unit system). First, define the reference frame (x-axis with origin). Then write the equation for the electric potential V (x) in chosen reference frame. Finally, calculate the electric potential in points A and B.

1. For three given electric charges (see the diagram below), calculate the total electric potential in points A and B using the superposition princi- ple. Give the answer in terms of Q and R, for ke = 1 a.u. (arbitrary unit system).
First, define the reference frame (x-axis with origin). Then write the equation for the electric potential V (x) in chosen reference frame. Finally, calculate the electric potential in points A and B.
2. For three given electric charges (see the diagram below), determine the direction and calculate the total electric field strength in points A and B using the superposition principle. Give the answer in terms of Q and R, for ke = 1 a.u. (arbitrary unit system).
Using the results of the previous problem, derive the equation for the electric field vector ~E(x). Then calculate the component of the the vector ~E(x) in given points A and B. Your final answer should be the direction and the magnitude of vector ~E(x).
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-m m mu uq1 = +4Q q2 = −Q q3 = −QA B R R R R
x
3. Three electric positive charges of equal charge q = 1.6 × 10−19 C are placed in the corners of a square with side R = 5× 10−10 m. One corner is vacant.
(a) Write the expression for the electric potential V (x, y) in any point (x, y) in the plane.
(b) Calculate the potential Vc(x, y) in the vacant corner of the square. Use ke = 9.0× 109 Nm2/C2 for the value of electrostatic constant.
You may have to define your own two-dimensional reference frame with the origin.