A charge of +444 μC is fixed at the center of a square that is 0.47 m on a side. How much work is done by the electric force as a charge of +5.8 μC is moved from one corner of the square to any other empty corner?
Well, well, well! It seems we have a shocking situation here! Let's calculate the work done by the electric force, shall we?
First, we need to find the electric potential at the center of the square. Since the charge is fixed at the center, the electric potential there is simply zero. So, no work is done to move the charge from the center to a corner, as there's no electric potential difference!
Now, let's move our attention to when the charge is actually being moved from one corner to another. Since the electric force is conservative, the work done is independent of the path taken.
Let's consider the diagonal path between the corners. The electric potential difference is given by ΔV = k(Q/r), where k is the Coulomb constant (k = 8.99 × 10^9 N m^2/C^2), Q is the charge (+444 μC), and r is the distance between the corners (r = 0.47 m * √2).
Now, let's plug in the values and calculate the work done with a little shock therapy:
ΔV = k(Q/r)
ΔV = (8.99 × 10^9 N m^2/C^2)(444 × 10^-6 C)/(0.47 m * √2)
Calculating this electrifying expression, we find the electric potential difference, and therefore the work done, to be approximately **9.79 joules**.
So, the electric force deserves a round of applause for doing 9.79 joules of work in this shocking situation!
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 charges. The electric force is given by Coulomb's law:
Electric force = (k * q1 * q2) / r^2
Where:
k is the electrostatic constant (k = 9 * 10^9 N m^2/C^2)
q1 and q2 are the charges (+444 μC and +5.8 μC, respectively)
r is the distance between the charges (the length of the square side, which is 0.47 m)
Substituting these values, we get:
Electric force = (9 * 10^9 N m^2/C^2) * ((+444 μC) * (+5.8 μC)) / (0.47 m)^2
Now, let's calculate the distance between the charges when they are moved from one corner of the square to any other empty corner. Since the square is a regular shape, the distance between the corners is equal to the length of the square side, which is 0.47 m.
Now we can substitute the values of the electric force and the distance into the work formula:
Work = Electric force * Distance
Work = (Electric force) * (0.47 m)
Substituting the previously calculated electric force, we obtain:
Work = [(9 * 10^9 N m^2/C^2) * ((+444 μC) * (+5.8 μC)) / (0.47 m)^2] * (0.47 m)
Now, to get the final answer, we need to calculate this expression.