Q1. What is the electric potential at the center of a cube of side-length 10 cm, if 8 point charges of 100 nC each are placed at the corners? The potential is defined to be zero at infinity.

Background

Topic: Electrostatics – Electric Potential due to Point Charges

This question tests your understanding of how to calculate the electric potential at a point due to multiple point charges, using the principle of superposition. The charges are symmetrically arranged at the corners of a cube, and you are asked to find the potential at the geometric center.

Key Terms and Formulas

• Electric Potential due to a Point Charge: The potential at a distance from a point charge is given by:

• is the permittivity of free space ()

• For multiple charges, potentials add algebraically:

• All charges are the same and equidistant from the center, so the calculation simplifies.

Step-by-Step Guidance

1. First, calculate the distance from the center of the cube to any corner. For a cube of side , this distance is .

2. Convert the side length to meters: , so meters.

3. Write the expression for the potential at the center due to one charge:

4. Since there are 8 identical charges, the total potential is .

5. Substitute the values: , , and as calculated above.

Try solving on your own before revealing the answer!