Advanced Practice Problems

1. Three charges are placed at the vertices of an equilateral triangle. Compute the net force on one charge and the net electric field at the center of the triangle.
2. Four point charges are located at the corners of a square. Calculate the net force on a fifth charge placed at the center of the square.
3. Determine the potential energy of a system of three charges placed at the corners of a triangle with sides 0.5 m, 0.6 m, and 0.7 m.
4. Two charges +3 μC and -3 μC are 0.6 m apart. Find the location along the line joining them where the net electric field is zero.
5. A charge +2 μC is placed inside a hollow spherical shell of radius 0.4 m carrying a uniform charge of -4 μC. Determine the net force on the inner charge.
6. Three charges lie on a straight line: +2 μC, -3 μC, +4 μC. Find the point where the net electric potential is zero.
7. Calculate the work required to assemble four point charges of +1 μC each at the corners of a square 0.5 m on a side.
8. Five charges of alternating signs are placed along a line. Compute the net force and net electric field at the center charge using vector addition.
9. A point charge +5 μC is placed at the origin. Determine the net force on a charge -2 μC at position (0.3 m, 0.4 m) using vector decomposition.
10. Derive the net electric field at the midpoint of a diagonal of a square with equal charges at the corners.