Two charged particles, q1 = −2.50×10−3 C and q2 = +3.700e-3 C, are separated by a distance of 5.00 cm. (a) What is the electric potential energy of this configuration? (b) What is the electric potential at a point midway between the particles?
I have the answer to a..which is -1.66e6, but I can get the correct answer for b
To calculate the electric potential at a point midway between two charged particles, you can use the equation for electric potential:
V = k * (q1 / r1 + q2 / r2)
where V is the electric potential, k is the Coulomb's constant (k = 8.99 x 10^9 Nm^2/C^2), q1 and q2 are the charges of the particles, and r1 and r2 are the distances from the point to each particle, respectively.
In this case, since the two particles are separated by a distance of 5.00 cm, the distance from the point to each particle is half of that, which is 2.50 cm or 0.0250 m.
Let's calculate the electric potential at the midpoint using these values:
q1 = -2.50 x 10^-3 C
q2 = +3.700 x 10^-3 C
r1 = r2 = 0.0250 m
k = 8.99 x 10^9 Nm^2/C^2
Plug in these values into the equation:
V = (8.99 x 10^9 Nm^2/C^2) * (-2.50 x 10^-3 C / 0.0250 m + 3.700 x 10^-3 C / 0.0250 m)
Calculating this expression:
V = (8.99 x 10^9 Nm^2/C^2) * (-0.100 C/m + 0.148 C/m)
V = (8.99 x 10^9 Nm^2/C^2) * (0.048 C/m)
V ≈ 4.315 x 10^8 Nm^2/C^2
Therefore, the electric potential at a point midway between the particles is approximately 4.315 x 10^8 Nm^2/C^2.
To determine the electric potential at a point midway between two charged particles, you need to calculate the electric potential due to each particle individually and then sum them up.
Here's how to approach the problem:
(a) Electric Potential Energy:
The electric potential energy of a configuration of two charged particles is given by the formula:
U = (k * |q1 * q2|) / r
where U is the electric potential energy, k is the electrostatic constant (k ≈ 8.99 × 10^9 Nm^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between them.
Plugging in the given values:
q1 = −2.50 × 10^−3 C
q2 = +3.700e^−3 C
r = 5.00 cm = 0.05 m
Using the formula above:
U = (8.99 × 10^9 Nm^2/C^2 * |-2.50 × 10^−3 C * +3.700e^−3 C|) / 0.05 m
U = 1.66 × 10^6 J (Note: The negative sign indicates that the potential energy is negative, indicating a net attractive force between the charged particles.)
So, you have the correct answer for part (a).
Now, let's move on to part (b):
(b) Electric Potential at Midway Point:
To calculate the electric potential at a point midway between two charged particles, you need to find the electric potential due to each particle individually at that point and then sum them up.
The electric potential V at a point due to a charged particle is given by the formula:
V = (k * q) / r
where V is the electric potential, k is the electrostatic constant, q is the charge of the particle, and r is the distance between the particle and the point.
For the particle q1:
q = −2.50 × 10^−3 C
r = half the distance between the particles = 0.025 m (half of 0.05 m)
Using the formula above:
V1 = (8.99 × 10^9 Nm^2/C^2 * -2.50 × 10^−3 C) / 0.025 m
For the particle q2:
q = +3.700e^−3 C
r = half the distance between the particles = 0.025 m (half of 0.05 m)
Using the formula above:
V2 = (8.99 × 10^9 Nm^2/C^2 * +3.700e^−3 C) / 0.025 m
Now, sum up the electric potentials from both particles:
V_total = V1 + V2
Calculate V_total using the values above, and you will find the electric potential at the midpoint between the particles.