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 need to consider the electric potential energy.
The formula for electric potential energy between two charges is given by:
U = (k * q1 * q2) / r
Where:
U is the electric potential energy,
k is the electrostatic constant (9 × 10^9 N m^2/C^2),
q1 and q2 are the magnitudes of the charges (in this case, 10 microC and -20 microC),
r is the distance between the charges (in this case, 0.35 m).
First, let's calculate the initial electric potential energy (U1) when the charges are 0.35 m apart:
U1 = (k * q1 * q2) / r
Substituting the values:
U1 = (9 × 10^9 N m^2/C^2) * (10 × 10^-6 C) * (-20 × 10^-6 C) / 0.35 m
Now, we need to find the electric potential energy (U2) when the distance between the charges is doubled (0.35 m * 2 = 0.70 m):
U2 = (k * q1 * q2) / r
Substituting the values:
U2 = (9 × 10^9 N m^2/C^2) * (10 × 10^-6 C) * (-20 × 10^-6 C) / 0.70 m
The work required to double the distance is given by the difference between the two potential energies:
Work = U2 - U1
Now you can substitute the values and calculate the work required to double the distance between the charges.