Two point charges each of magnitude 2.14 µC are located on the x axis. One is at x = 1.00 m and the other is at x = -1.00 m.
(a) Determine the electric potential on the y axis at y = 0.620 m.
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(b) Calculate the change in electric potential energy of the system as a third charge of +3.63 µC is brought from infinitely far away to a position on the y axis at y = 0.620 m.
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To solve this problem, we need to apply the concept of electric potential and electric potential energy.
(a) To determine the electric potential on the y axis at y = 0.620 m, we need to calculate the contributions from both point charges and then sum them up.
The electric potential due to a point charge can be calculated using the formula:
V = k * q / r
where:
V is the electric potential,
k is the Coulomb's constant (9 x 10^9 Nm^2/C^2),
q is the magnitude of the charge, and
r is the distance from the charge to the point where we are measuring the potential.
Let's calculate the electric potential due to each charge separately:
For the charge at x = 1.00 m:
q = 2.14 µC = 2.14 x 10^-6 C
r = √((x - x1)^2 + y^2) = √((0 - 1)^2 + (0.620)^2) = 0.808 m
V1 = k * q / r
For the charge at x = -1.00 m:
q = 2.14 µC = 2.14 x 10^-6 C
r = √((x - x2)^2 + y^2) = √((0 + 1)^2 + (0.620)^2) = 1.324 m
V2 = k * q / r
Now, we sum up the electric potentials from both charges to get the total electric potential at y = 0.620 m:
V_total = V1 + V2
Calculate V_total using the given values and the formula for electric potential.
(b) To calculate the change in electric potential energy of the system as a third charge of +3.63 µC is brought from infinitely far away to a position on the y axis at y = 0.620 m, we need to find the difference between the electric potential energy at the initial and final positions of the third charge.
The change in electric potential energy (ΔU) can be calculated using the formula:
ΔU = q3 * ΔV
where:
ΔU is the change in electric potential energy,
q3 is the magnitude of the third charge (3.63 µC = 3.63 x 10^-6 C), and
ΔV is the change in electric potential energy, which is the difference between the electric potentials at the two positions.
Calculate ΔV using the electric potentials from part (a):
ΔV = V_final - V_initial = V_final - V_inf
V_final is the electric potential at y = 0.620 m (calculated in part (a)), and V_inf is the electric potential when the charge is infinitely far away, which is essentially zero.
Now, calculate ΔU using the given values and the formula for change in electric potential energy.
Substitute the values and calculate both (a) and (b).