Two point charges, +3.09 µC and -5.65 µC, are separated by 1.19 m. What is the electric potential midway between them
To find the electric potential midway between the two point charges, you can use the formula for the electric potential due to a point charge. The electric potential at a point P due to a point charge Q is given by:
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 of the point charge
- r is the distance between the point charge and point P
Since you have two point charges, the electric potential at point P due to both charges will be the sum of the electric potentials due to each charge.
Let's calculate the electric potential due to the positive charge first:
V1 = k * Q1 / r1
Given:
Q1 = +3.09 µC
r1 = half the distance between the charges, which is 1.19 m / 2 = 0.595 m (since point P is halfway between the charges)
Now, let's calculate the electric potential due to the negative charge:
V2 = k * Q2 / r2
Given:
Q2 = -5.65 µC
r2 = half the distance between the charges, which is also 1.19 m / 2 = 0.595 m
Since the electric potential midway between the charges is the sum of V1 and V2, we can calculate it as follows:
V_midway = V1 + V2
Just substitute the given values into the formulas and solve for V_midway.
It's important to note that electric potential is a scalar quantity, so the sign indicates the sign of the potential.
To calculate the electric potential midway between two point charges, we can use the formula:
V = k * q1 / r1 + k * q2 / r2
Where:
V is the electric potential,
k is the Coulomb's constant (k = 9 × 10^9 N m^2/C^2),
q1 and q2 are the magnitudes of the charges, and
r1 and r2 are the distances from the midpoint to the charges.
Given:
q1 = +3.09 µC,
q2 = -5.65 µC,
r1 = r2 = 1.19 m.
Let's substitute the values into the formula:
V = (9 × 10^9 N m^2/C^2) * (+3.09 µC / 1.19 m) + (9 × 10^9 N m^2/C^2) * (-5.65 µC / 1.19 m)
V = (9 × 10^9 N m^2/C^2) * (3.09 × 10^-6 C / 1.19 m) + (9 × 10^9 N m^2/C^2) * (-5.65 × 10^-6 C / 1.19 m)
V ≈ 2.77 × 10^6 V + (-5.68 × 10^6 V)
V ≈ -2.91 × 10^6 V
Therefore, the electric potential midway between the two point charges is approximately -2.91 × 10^6 V.