Two point charges, +3.63 µC and -5.95 µC, are separated by 1.18 m. What is the electric potential midway between them?
k*10^-6*[3.63/0.59 - 5.95/0.59] Volts
where k is the Coulomb's Law constant.
To find the electric potential midway between two point charges, we can use the formula for electric potential due to a point charge:
V = k * q / r
where V is the electric potential, k is the Coulomb's constant (8.99 x 10^9 N m^2/C^2), q is the charge, and r is the distance between the charges.
Let's calculate the electric potential due to each charge separately:
For the positive charge (+3.63 µC), the electric potential is:
V1 = k * q / r
= (8.99 x 10^9 N m^2/C^2) * (3.63 x 10^-6 C) / (1.18 m)
For the negative charge (-5.95 µC), the electric potential is:
V2 = k * q / r
= (8.99 x 10^9 N m^2/C^2) * (-5.95 x 10^-6 C) / (1.18 m)
Now, to find the electric potential midway between them, we need to add the individual electric potentials together and divide by 2:
V_midway = (V1 + V2) / 2
Let's plug in the values and calculate:
V_midway = (V1 + V2) / 2
= ((8.99 x 10^9 N m^2/C^2) * (3.63 x 10^-6 C) / (1.18 m) + (8.99 x 10^9 N m^2/C^2) * (-5.95 x 10^-6 C) / (1.18 m)) / 2
= (8.99 x 10^9 N m^2/C^2) * ((3.63 x 10^-6 C) - (5.95 x 10^-6 C)) / (1.18 m) / 2
Simplifying this expression will give us the electric potential midway between the two point charges.
To find the electric potential midway between two point charges, we need to calculate the electric potential contribution from each charge separately and then add them together.
The electric potential at a point due to a point charge can be calculated using the formula:
V = k * (Q / r)
Where:
V is the electric potential,
k is Coulomb's constant (9.0 * 10^9 Nm^2/C^2),
Q is the charge, and
r is the distance from the charge to the point.
Let's calculate the electric potential due to the first charge (+3.63 µC) at the midway point:
Q1 = +3.63 µC
r1 = 0.59 m (half of the total distance between the charges, as it's the midway point)
V1 = k * (Q1 / r1)
= (9.0 * 10^9 Nm^2/C^2) * ((3.63 * 10^-6 C) / (0.59 m))
Now, let's calculate the electric potential due to the second charge (-5.95 µC) at the same midway point:
Q2 = -5.95 µC
r2 = 0.59 m (same distance as before)
V2 = k * (Q2 / r2)
= (9.0 * 10^9 Nm^2/C^2) * ((-5.95 * 10^-6 C) / (0.59 m))
Finally, we can find the electric potential midway between the charges by adding up the contributions:
V_midway = V1 + V2
Now, let's calculate the value.