Question

Four equal +6.00-μC point charges are placed at the corners of a square 2.00 m on each side. What is the electric potential (relative to infinity) due to these charges at the center of this square?

Answer 1

The electric potential at the center of a square due to four equal point charges is calculated using Coulomb's constant, the charge value, and the distance from the charge to the point of interest, with the total potential being four times the potential due to one charge.

Step-by-step explanation:

The student has asked about the electric potential at the center of a square due to four equal point charges placed at the corners. The electric potential due to a single point charge is given by the formula V = kQ/r, where V is the electric potential, k is Coulomb's constant (8.988 × 109 N·m²/C2), Q is the charge, and r is the distance from the charge to the point of interest. In the scenario provided, each charge is +6.00-μC and the side of the square is 2.00 m. The distance from a corner to the center (r) can be calculated using the Pythagorean theorem, resulting in r = √(1² + 1²) = √2 m. The potential at the center due to one charge is V = kQ/r, and since all four charges are equal and at the same distance from the center, the total potential will be four times the potential due to one charge. Therefore, the electric potential at the center is V = 4 × (kQ/√2).

Answer 2

The electric potential at the center of the square due to the four +6.00-μC point charges is
`\(2.70 * 10^4\)` volts.

Step-by-step explanation:

The electric potential V at the center of the square can be calculated by summing the electric potentials contributed by each point charge. The electric potential due to a point charge is given by V =
`(kQ)/(r)\)`, where k is Coulomb's constant
`(\(8.99 * 10^9 \, \text{N m}^2/\text{C}^2\))`, Q is the charge, and r is the distance from the charge to the point where potential is being calculated.

In this case, there are four point charges at the corners of a square. The distance from the center of the square to each corner is the side length divided by the square root of 2 (2.00,
`\text{m}/√(2)\))`. Summing up the potentials from all four charges yields the total electric potential at the center of the square.

Understanding the principles of electric potential due to point charges and the process of calculating the total potential at a point in a system of multiple charges.