two electric charges +10 microC and -20microC are located .35 m apart how much work is required to double the distance between them?
To find the work required to double the distance between two electric charges, we can use the equation for the electric potential energy.
The electric potential energy between two point charges is given by the formula:
U = k * (q1 * q2) / r
Where:
U is the electric potential energy
k is the electrostatic constant (k ≈ 8.99 x 10^9 Nm^2/C^2)
q1 and q2 are the magnitudes of the charges
r is the distance between the charges
In this case, we have two charges: +10 µC and -20 µC, and the distance is 0.35 m.
First, we need to calculate the initial electric potential energy (U_initial) using the given values. Then, we will double the distance, which will change the distance between the charges to 2 times its initial value. Using this new distance, we will calculate the final electric potential energy (U_final).
Let's calculate step by step:
1. Calculate the initial electric potential energy:
U_initial = k * (q1 * q2) / r
q1 = +10 µC = 10 x 10^-6 C
q2 = -20 µC = -20 x 10^-6 C
r = 0.35 m
U_initial = 8.99 x 10^9 Nm^2/C^2 * [(10 x 10^-6 C) * (-20 x 10^-6 C)] / 0.35 m
2. Double the distance:
New distance = 2 * 0.35 m = 0.70 m
3. Calculate the final electric potential energy:
U_final = k * (q1 * q2) / r
q1 = +10 µC = 10 x 10^-6 C
q2 = -20 µC = -20 x 10^-6 C
r = 0.70 m
U_final = 8.99 x 10^9 Nm^2/C^2 * [(10 x 10^-6 C) * (-20 x 10^-6 C)] / 0.70 m
4. Calculate the work required to double the distance:
Work = U_final - U_initial
Now you can substitute the values into the equation to find the work required to double the distance between the charges.