Suppose q1 = +2.90 µC is no longer at y = 0.300 m, but is now at y = 0.244 m. The charge q2 = +2.90 µC is at x = 0 and y = 0.500 m, and the point 3 is at x = y = 0.500 m.
To find the electric potential at point 3 due to the charges q1 and q2, we can use the formula for electric potential due to multiple point charges. The general formula is:
V = k * (q1 / r1 + q2 / r2 + q3 / r3 + ...)
Where V is the electric potential, k is the Coulomb's constant (9 × 10^9 Nm^2/C^2), q1, q2, q3, etc. are the charges, and r1, r2, r3, etc. are the distances between each charge and the point at which the electric potential is being measured.
In this case, we have two charges: q1 = +2.90 µC and q2 = +2.90 µC.
The distances between the charges and point 3 are as follows:
- Distance between q1 and point 3 (r1): This is the difference in y-coordinates, which is 0.244 m - 0.5 m = -0.256 m (negative sign indicates the direction from q1 to point 3).
- Distance between q2 and point 3 (r2): This is the square root of ((0.5 m)^2 + (0.5 m)^2) = 0.707 m.
Now substitute these values into the formula:
V = k * (q1 / r1 + q2 / r2)
= (9 × 10^9 Nm^2/C^2) * ((+2.90 µC) / (-0.256 m) + (+2.90 µC) / (0.707 m))
Calculating the values in the parentheses gives:
V = (9 × 10^9 Nm^2/C^2) * (-11.33 µC/m + 4.10 µC/m)
Now, let's simplify and calculate the result:
V = (9 × 10^9 Nm^2/C^2) * (-7.23 µC/m)
= - 6.51 × 10^7 V
Therefore, the electric potential at point 3 due to the charges q1 and q2 is approximately -6.51 × 10^7 V.