If the electric potential energy between two charges of 1.5C and 6.0 C is 0.16 J, what is their separation?
thanx elena :-)
To find the separation between two charges given the electric potential energy, we can use the formula for electric potential energy. The formula is:
Electric Potential Energy = (k * |q1 * q2|) / r
where k is the electrostatic constant (9 * 10^9 Nm^2/C^2), q1 and q2 are the charges in coulombs, and r is the separation distance in meters.
In this case, we are given the electric potential energy (0.16 J), the charges (1.5 μC and 6.0 μC), and we need to find the separation distance (r).
We need to convert the charges from microcoulombs (μC) to coulombs (C) by dividing them by 10^6:
q1 = 1.5 μC = 1.5 * 10^(-6) C
q2 = 6.0 μC = 6.0 * 10^(-6) C
Now we can rearrange the formula to solve for r:
r = (k * |q1 * q2|) / Electric Potential Energy
Substituting the known values:
r = (9 * 10^9 Nm^2/C^2 * |1.5 * 10^(-6) C * 6.0 * 10^(-6) C|) / (0.16 J)
By simplifying the expression inside the absolute value and performing the calculation, we get:
r ≈ 1.39 meters
Therefore, the separation between the charges is approximately 1.39 meters.
PE = k•q²/r,
r= k•q²/PE,
where
k =9•10^9 N•m²/C².