Two identical point charges are fixed to diagonally opposite corners of a square that is .5m on a side. Each charge is 3.0E-6 C. How much work is done by the electric force as one of the charges moves to an empty corner?
To find the work done by the electric force as one charge moves to an empty corner, we need to calculate the change in electric potential energy.
The electric potential energy between two point charges can be calculated using the formula:
PE = k * (q1 * q2) / r
Where:
- PE is the electric potential energy
- k is the electrostatic constant (which equals 9.0 x 10^9 N m^2/C^2)
- q1 and q2 are the charges
- r is the distance between the charges
In this case, we have two identical charges (3.0E-6 C) fixed to diagonally opposite corners of a square that is 0.5 m on each side. The distance between the charges can be calculated using the Pythagorean theorem, since it forms a right-angled triangle with each side of the square.
Let's calculate the distance (r):
r = √(0.5^2 + 0.5^2)
r = √(0.25 + 0.25)
r = √(0.5)
r ≈ 0.71 m
Now we can calculate the initial electric potential energy (PE_initial) with both charges on diagonally opposite corners:
PE_initial = k * (q1^2) / r
PE_initial = (9.0 x 10^9) * (3.0E-6^2) / 0.71
Next, when one of the charges moves to an empty corner, the new distance (r_new) will be the diagonal of the square, which can be calculated using the Pythagorean theorem again:
r_new = √(0.5^2 + 0.5^2)
r_new = √(0.25 + 0.25)
r_new = √(0.5)
r_new ≈ 0.71 m
The final electric potential energy (PE_final) with one charge at an empty corner can be calculated as follows:
PE_final = k * (q1 * q2) / r_new
PE_final = (9.0 x 10^9) * (3.0E-6 * 3.0E-6) / 0.71
Finally, the work done by the electric force is the difference between the initial and final electric potential energies:
Work = PE_final - PE_initial
By plugging in the values and performing the calculations, you can find the work done by the electric force as one of the charges moves to an empty corner.