Two point charges, +3.90 ìC and -7.50 ìC, are separated by 3.30 m. What is the electric potential midway between them?
To find the electric potential midway between two point charges, we can use the formula for the electric potential due to a point charge. The electric potential, also known as voltage, at a point in space is given by:
V = k * (q / r)
Where:
V is the electric potential or voltage,
k is Coulomb's constant (9 x 10^9 N m^2/C^2),
q is the charge of the point charge,
r is the distance from the point charge.
In this case, we have two point charges, +3.90 ìC and -7.50 ìC, separated by 3.30 m. Since we want to find the electric potential midway between them, the distance from each charge to the midpoint is halved, which gives us a distance of 3.30 m / 2 = 1.65 m from each point charge to the midway point.
Let's calculate the electric potential due to each charge individually:
For the positive charge (q = +3.90 ìC):
V1 = k * (q / r1) = (9 x 10^9 N m^2/C^2) * (3.90 x 10^-6 C / 1.65 m)
For the negative charge (q = -7.50 ìC):
V2 = k * (q / r2) = (9 x 10^9 N m^2/C^2) * (-7.50 x 10^-6 C / 1.65 m)
Finally, to find the electric potential at the midway point, we add the two individual electric potentials:
V_midway = V1 + V2
Now, let's substitute the values into the formulas to find the electric potential midway between the charges.