A charge of +355 μC is fixed at the center of a square that is 0.64 m on a side. How much work is done by the electric force as a charge of +7.9 μC is moved from one corner of the square to any other empty corner?
To calculate the work done by the electric force, we can use the equation:
Work = Electric force × Distance
First, let's find the electric force between the two charges. The electric force is given by Coulomb's Law:
Electric force = (k × q1 × q2)/r^2
where k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between them.
In this case, q1 = +355 μC and q2 = +7.9 μC.
Calculating the electric force:
Electric force = (8.99 x 10^9 N m^2/C^2) × (+355 μC) × (+7.9 μC) / (0.64 m)^2
Next, we need to find the distance between the charges. Since the charges are at the corners of the square, the distance between them is the length of the diagonal of the square.
Using the Pythagorean theorem, we can calculate the diagonal:
Diagonal = sqrt(0.64 m^2 + 0.64 m^2)
Now that we have the electric force and distance, we can calculate the work done:
Work = Electric force × Distance
Plug in the values and calculate the work.
To calculate the work done by the electric force, we can use the formula:
Work = Electric force × Distance
First, let's calculate the electric force between the two charges using Coulomb's Law:
Electric force = k × (q1 × q2) / r^2
Where:
- k is the electrostatic constant, approximately 9 × 10^9 N m^2/C^2
- q1 and q2 are the charges (+355 μC and +7.9 μC, respectively)
- r is the distance between the charges
Given that the distance between any two corners of a square is the same (0.64 m), we can use this distance for 'r' in the equation.
Substituting the values into the equation:
Electric force = (9 × 10^9 N m^2/C^2) × ((+355 μC) × (+7.9 μC)) / (0.64 m)^2
Now, let's calculate the electric force.
Electric force = (9 × 10^9) × ((355 × 10^-6) × (7.9 × 10^-6)) / (0.64)^2
Electric force = (9 × 10^9) × (2.8025 × 10^-12) / 0.4096
Electric force ≈ 1.854 × 10^-3 N
Now that we have the electric force, let's calculate the work done.
Work = Electric force × Distance
The distance between the corners of the square is the length of one side, which is 0.64 m.
Work = (1.854 × 10^-3 N) × (0.64 m)
Work ≈ 1.186 × 10^-3 J
Therefore, approximately 1.186 × 10^-3 Joules of work is done by the electric force as the charge is moved from one corner to another.