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? Assume the potential is zero at infinity.

Background

Topic: 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, the total potential is the sum of the potentials from each charge (superposition principle):

Step-by-Step Guidance

1. First, recognize that all 8 charges are identical and equidistant from the center of the cube. So, the potential at the center is 8 times the potential due to one charge at that distance.

2. Calculate the distance from a corner of the cube to the center. For a cube of side , this distance is . Here, cm m, so m.

3. Write the expression for the total potential at the center:

4. Substitute the values: nC C, C/N·m, and as calculated above.

Try solving on your own before revealing the answer!