Two point charges of +1.0 uC and -2.0 uC are located 0.50 m apart. What is the minimum amount of work needed to move the charges apart to double the distance between them? (k=8.99x10^9Nm^2/C^2)

No answer

To calculate the minimum amount of work needed to move the charges apart and double the distance between them, we can use the equation for the electric potential energy.

The electric potential energy (U) between two point charges can be calculated using the formula:

U = (k * q1 * q2) / r

Where:
U is the electric potential energy
k is the electrostatic constant with a value of 8.99 x 10^9 Nm^2/C^2
q1 and q2 are the magnitudes of the two charges
r is the distance between the charges

In this case, the initial distance between the charges is 0.50m. To double the distance, we need to move the charges to a distance of 2 * 0.50m = 1.00m.

Now let's calculate the initial electric potential energy (U_initial) when the charges are 0.50m apart:

U_initial = (k * q1 * q2) / r_initial

Substituting the given values:
k = 8.99 x 10^9 Nm^2/C^2
q1 = +1.0 uC = +1.0 x 10^-6 C
q2 = -2.0 uC = -2.0 x 10^-6 C
r_initial = 0.50m

U_initial = (8.99 x 10^9 Nm^2/C^2)(1.0 x 10^-6 C)(-2.0 x 10^-6 C) / 0.50m

Next, let's calculate the final electric potential energy (U_final) when the charges are 1.00m apart:

U_final = (k * q1 * q2) / r_final

Substituting the given values:
k = 8.99 x 10^9 Nm^2/C^2
q1 = +1.0 uC = +1.0 x 10^-6 C
q2 = -2.0 uC = -2.0 x 10^-6 C
r_final = 1.00m

U_final = (8.99 x 10^9 Nm^2/C^2)(1.0 x 10^-6 C)(-2.0 x 10^-6 C) / 1.00m

Finally, the minimum amount of work needed to move the charges apart to double the distance between them is given by:

Work = U_final - U_initial

Now you can substitute the values and calculate the work.