Two charges q = 3.0ì C are fixed in space a distance d = 4.5 cm apart. With V = 0 at infinity, What is the potential energy U of the three-charge configuration when the third charge is in place?
Where is the third charge located?
What does the ì symbol mean? micro?
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To determine the potential energy U of the three-charge configuration, we need to calculate the potential energy of each pair of charges and then sum them up.
The potential energy between two charges is given by the equation:
U = (k * q1 * q2) / r
Where:
U = potential energy
k = electrostatic constant = 8.99 × 10^9 N m^2/C^2
q1 and q2 = charges of the two particles
r = distance between the charges
In this case, we have two fixed charges q situated a distance d apart. The third charge q3 will be placed in between them.
To find the potential energy U of the three-charge configuration, we need to calculate the potential energy between q1 and q3, between q2 and q3, and the potential energy between q1 and q2 (since they are fixed in place).
1. Potential energy between q1 and q3:
Using the formula U = (k * q1 * q3) / r1, where r1 is the distance between q1 and q3 (which will be equal to d/2), we can calculate the potential energy between q1 and q3.
2. Potential energy between q2 and q3:
Using the same formula U = (k * q2 * q3) / r2, where r2 is the distance between q2 and q3 (which will also be equal to d/2), we can calculate the potential energy between q2 and q3.
3. Potential energy between q1 and q2:
Since q1 and q2 are fixed, the potential energy between them is constant and does not depend on the position of q3. Therefore, we can calculate this potential energy assuming q3 is not present.
Finally, we can sum up the potential energies calculated in steps 1, 2, and 3 to find the total potential energy U of the three-charge configuration.
Note: Make sure to convert the distance d from cm to meters before performing the calculations.