A 5.0-nC charge is at (0, 0) and a -2.0-nC charge is at (3.0 m, 0). If the potential is taken to be zero at infinity, what is the electric potential energy of a 1.0-nC charge at point (0, 4.0 m)?
Answer
1.5 × 10-8 J
3.6 × 10-9 J
1.1 × 10-8 J
7.7 × 10-9 J
Well, let me tell you a shocking answer! The electric potential energy of a 1.0-nC charge at point (0, 4.0 m) is 1.1 × 10-8 J. That's a lot of potential for some electrifying fun!
To calculate the electric potential energy of a 1.0-nC charge at point (0, 4.0 m), we can use the formula:
Electric potential energy = (k * Q1 * Q2) / r
Where:
- k is the electrostatic constant (9.0 × 10^9 N*m^2/C^2)
- Q1 is the charge of the first object (5.0 × 10^-9 C)
- Q2 is the charge of the second object (1.0 × 10^-9 C)
- r is the distance between the charges (in this case, it is the distance between (0, 0) and (0, 4.0 m))
First, let's calculate the distance between the two charges:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Distance = sqrt((0 - 0)^2 + (4.0 m - 0)^2)
Distance = sqrt(0 + 16.0 m^2)
Distance = sqrt(16.0) m
Distance = 4.0 m
Now we can substitute the values into the formula:
Electric potential energy = (k * Q1 * Q2) / r
Electric potential energy = (9.0 × 10^9 N*m^2/C^2) * (5.0 × 10^-9 C) * (1.0 × 10^-9 C) / (4.0 m)
Electric potential energy = (45.0 × 10^0 N*m^2) / (4.0 m)
Electric potential energy = 11.25 × 10^0 N*m
Electric potential energy = 1.125 × 10^1 N*m
Electric potential energy = 1.125 J
Therefore, the electric potential energy of a 1.0-nC charge at point (0, 4.0 m) is 1.125 J. However, none of the provided answer choices match this calculation.
To find the electric potential energy of a charge at a specific point, you can use the formula:
Electric Potential Energy = (k * q1 * q2) / r
where k is the Coulomb's constant (9 × 10^9 N * m^2 / C^2), q1 and q2 are the charges in coulombs, and r is the distance between the charges in meters.
In this case, the charge q1 is 1.0-nC, and the charge q2 is 5.0-nC. The distance between them is the distance between the points (0, 0) and (0, 4.0 m), which is 4.0 m.
Substituting these values into the formula, we get:
Electric Potential Energy = (9 × 10^9 N * m^2 / C^2) * (1.0 × 10^-9 C) * (5.0 × 10^-9 C) / (4.0 m)
Simplifying the calculation:
Electric Potential Energy = (9 × 1.0 × 5.0) / (4.0) * 10^9 * 10^-9 = 11.25 × 10^-8 J
So, the electric potential energy of the 1.0-nC charge at point (0, 4.0 m) is 1.125 × 10^-7 J.
However, none of the provided answers match this result. Please check your calculations or provide more information if necessary.