A point charge of -7.9 microcoulomb is at the origin.
What is the electric potential at (3.0, - 3.0)?
-kQ/sqrt(3^2 + (-3)^2) = -kQ/sqrt18
k is the Colulomb constant
Q = -7.9*10^-6 C
To calculate the electric potential at a point due to a point charge, you can use the formula:
V = k * (q / r)
where V is the electric potential, k is the electrostatic constant (9.0 x 10^9 N m^2/C^2), q is the charge, and r is the distance between the charge and the point.
In this case, the charge is -7.9 microcoulomb and the point is (3.0, -3.0), which means the distance is the distance from the origin to the point. We can use the distance formula to find the distance:
r = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )
Substituting the coordinates, we get:
r = sqrt( (3.0 - 0)^2 + (-3.0 - 0)^2 )
Simplifying:
r = sqrt( 3^2 + (-3)^2 )
r = sqrt( 9 + 9 )
r = sqrt( 18 )
r ≈ 4.2426
Now, we can calculate the electric potential:
V = (9.0 x 10^9 N m^2/C^2) * (-7.9 x 10^-6 C) / 4.2426
Simplifying:
V ≈ (-7.11 x 10^(-5) N m) / 4.2426
V ≈ -1.675 x 10^(-5) N m
Therefore, the electric potential at (3.0, -3.0) due to the -7.9 microcoulomb point charge at the origin is approximately -1.675 x 10^(-5) N m.