Two particles with Q1 = 40 µC and Q2 = 87 µC are initially separated by a distance of 2.6 m and then brought closer together so that the final separation is 1.7 m. What is the change in the electric potential energy?
To calculate the change in electric potential energy, we can use the formula:
ΔU = U_f - U_i
where ΔU represents the change in electric potential energy, U_f is the final electric potential energy, and U_i is the initial electric potential energy.
The electric potential energy between two particles can be calculated using the formula:
U = k * (|Q1| * |Q2|) / r
where k is the Coulomb's constant (k = 9 × 10^9 N m^2/C^2), |Q1| and |Q2| are the magnitudes of the charges, and r is the distance between the particles.
Let's calculate the initial and final electric potential energies:
U_i = k * (|Q1| * |Q2|) / r_i
U_f = k * (|Q1| * |Q2|) / r_f
Substituting the given values:
U_i = (9 × 10^9 N m^2/C^2) * (40 × 10^-6 C * 87 × 10^-6 C) / 2.6 m
U_f = (9 × 10^9 N m^2/C^2) * (40 × 10^-6 C * 87 × 10^-6 C) / 1.7 m
Now, we can calculate the change in electric potential energy:
ΔU = U_f - U_i
Just substitute the values for U_f and U_i into the equation and solve for ΔU:
ΔU = [(9 × 10^9 N m^2/C^2) * (40 × 10^-6 C * 87 × 10^-6 C) / 1.7 m] - [(9 × 10^9 N m^2/C^2) * (40 × 10^-6 C * 87 × 10^-6 C) / 2.6 m]