Q1. What is the electric potential at the center of a cube if 8 point charges (each 100 nC) are placed at the corners of a cube with side length 10 cm, and the potential is defined as zero at infinity?

Background

Topic: Electrostatics – Electric Potential

This question tests your understanding of how to calculate the electric potential at a point due to multiple point charges, specifically using the principle of superposition and the formula for electric potential from a point charge.

Key Terms and Formulas

• Electric potential (): The work needed to bring a unit positive charge from infinity to a point in space.

• Superposition principle: The total potential at a point is the sum of the potentials due to each charge.

• Formula for potential from a point charge:

• = charge at corner

• = permittivity of free space ()

• = distance from charge to the center of the cube

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 the sum of the potentials from each charge.

2. Calculate the distance from a corner to the center of the cube. For a cube of side , the distance is , but since the side length is 10 cm, convert to meters: m.

3. Plug in the values for nC ( C), , and into the formula for each charge, then multiply by 8 (since there are 8 charges).

4. Set up the expression for the total potential at the center:

Where meters.

Try solving on your own before revealing the answer!