Four point charges, each with Q = 7.2 µC, are arranged at the corners of a square of edge length 3.6 m. What is the electric potential at the center of the square?
1 V
Find the potential from one corner, then multipy it by 4. Potential is a scalar, so it can be added.
V(one corner)=kQ/(3.6*sqrt2)
To find the electric potential at the center of the square, we can use the principle of superposition. The superposition principle states that the total electric potential at a point due to a system of charges is equal to the algebraic sum of the electric potentials produced by each individual charge.
So, let's calculate the electric potential at the center of the square:
1. First, we need to determine the distance between the center of the square and each of the four charges. Since the square is of edge length 3.6 m, the distance from the center to each charge will be half of the diagonal of the square. diagonals of a square are equal, therefore, each diagonal has a length of 3.6 m. So, the distance from the center of the square to each charge is 1.8 m.
2. Now, we can calculate the electric potential produced by each individual charge. The electric potential due to a point charge can be calculated using the formula:
V = k * Q / r,
where V is the electric potential, k is Coulomb's constant (approximately 9 × 10^9 Nm²/C²), Q is the charge magnitude, and r is the distance between the charge and the point where we want to calculate the potential.
3. Plugging in the values, we have:
V = (9 × 10^9 Nm²/C²) * (7.2 × 10^-6 C) / (1.8 m)
V = 32 Nm²/C
4. Finally, since there are four charges at the corners of the square, we need to add up the electric potentials from each charge to find the total electric potential at the center. Since the electric potentials are scalar quantities, we can simply add them algebraically:
V_total = 4 * (32 Nm²/C)
V_total = 128 Nm²/C
So, the electric potential at the center of the square is 128 Nm²/C, which can be represented as 128 V. Therefore, the correct answer is 128 V.