IB Physics Point Charges at the Corners of a Square

This sheet practices finding the electric potential of a system of point charges.

1. Define electric potential at a point in an electric field.
2. A point charge -q is placed at (-d/2,0) and a point charge +q is placed at (d/2,0). Find the electric potential at the point P that has coordinates (2d,0).
3. In question 2 the point P is moved to a very large distance x from the origin along the x-axis. Show that the potential at P is approximately d k q/x².
4. In question 2 find the electrostatic potential energy of the two charge system. What does this mean?
5. Point charges of +q are placed at the corners of a square of side of length d. Find the electric potential at the centre of the square.
6. In question 5 sketch a graph showing the variation in electric potential along the y-axis. The origin is at the centre of the square and the y-axis is parallel to the side of the square.
7. Show that the potential at the point (x,y) near the origin is approximately V = 8kq/d(1 + ( x² + y² )/d² + ..).
8. In question 5 a charge +q is placed at the origin and given a small displacement along the y-axis. Describe the subsequent motion of this charge and calculate its period. The charges at the four corners of the square are fixed in position.