Two 2.46uC point charges are located on the x axis. One is at x = 1.01m, and the other is at x = -1.01m. Determine the electric field on the y axis at y = 0.455m & Calculate the electric force on a -2.82uC charge placed on the y axis at y = 0.455m
I'm using E=kq/r^2 and F=kqq/r^2 and my r I found to be 1.108... but I can't seem to figure out what I keep getting wrong... Maybe a vector adding error?
idk bro
To calculate the electric field and force correctly, it is important to consider the vector nature of these quantities. Let's break down the problem step-by-step:
Step 1: Calculate the electric field on the y-axis at y = 0.455m.
Given:
Charge 1 (q1) = 2.46 μC
Charge 2 (q2) = 2.46 μC
Charge 3 (q3) = -2.82 μC
Distance from Charges 1 & 2 (r₁₂) = 2.02 m (1.01 m + 1.01 m)
Distance from Charge 1 to y-axis (r₁₃) = 1.01 m
Formula: Electric Field (E) = k * q / r^2
Where:
k = 8.99 × 10^9 Nm^2/C^2 (Coulomb's constant)
q = magnitude of the charge
r = distance from the charge to the point of interest
To calculate the electric field at y = 0.455 m, we need to consider the contributions from charges 1 and 2 separately and then sum them up.
Electric field due to charge 1:
E₁ = k * q₁ / r₁₃^2
E₁ = (8.99 × 10^9 Nm²/C²) * (2.46 × 10^-6 C) / (1.01 m)^2
Electric field due to charge 2:
E₂ = k * q₂ / r₁₃^2
E₂ = (8.99 × 10^9 Nm²/C²) * (2.46 × 10^-6 C) / (1.01 m)^2
Step 2: Calculate the net electric field by summing the contributions:
Total electric field at y = 0.455 m will be the vector sum of E₁ and E₂:
E_total = E₁ + E₂
Step 3: Calculate the electric force on the -2.82 μC charge placed at y = 0.455 m.
Formula: Electric Force (F) = k * q₁ * q₂ / r^2
In this case, we need to consider the force between the newly placed charge (q₃) and the other charges.
Electric force between charge 1 and charge 3:
F₁₃ = k * q₁ * q₃ / r₁₃^2
F₁₃ = (8.99 × 10^9 Nm²/C²) * (2.46 × 10^-6 C) * (-2.82 × 10^-6 C) / (1.01 m)^2
Electric force between charge 2 and charge 3:
F₂₃ = k * q₂ * q₃ / r₁₃^2
F₂₃ = (8.99 × 10^9 Nm²/C²) * (2.46 × 10^-6 C) * (-2.82 × 10^-6 C) / (1.01 m)^2
The total electric force on the -2.82 μC charge will be the vector sum of F₁₃ and F₂₃:
F_total = F₁₃ + F₂₃
By following these steps and applying the correct vector addition, you should be able to accurately calculate the electric field and electric force in the given scenario.
To determine the electric field on the y-axis at y = 0.455m, you need to calculate the electric field contribution from each of the two point charges. Since the charges are positioned on the x-axis, the electric field along the y-axis will be due to the y-components of the electric fields from each charge.
Using Coulomb's law, the formula to calculate the electric field at a point P due to a point charge q is:
E = (k * q) / r^2
where E is the electric field, k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the charge to the point P.
For the point charge at x = 1.01m, the distance, r1, from the charge to P is:
r1 = √(x^2 + y^2) = √((1.01m)^2 + (0.455m)^2)
Similarly, for the point charge at x = -1.01m, the distance, r2, from the charge to P is:
r2 = √((-1.01m)^2 + (0.455m)^2)
Now you can calculate the electric field, E1, at point P due to the charge at x = 1.01m:
E1 = (k * q) / r1^2
And the electric field, E2, at point P due to the charge at x = -1.01m:
E2 = (k * q) / r2^2
Finally, you need to determine the net electric field at point P by adding the y-components of the electric fields from both charges:
E_net = E1 + E2
This will give you the magnitude and direction of the electric field on the y-axis at y = 0.455m.
To calculate the electric force on a charge of -2.82uC placed at y = 0.455m, you can use the formula for the electric force between two point charges:
F = (k * q1 * q2) / r^2
where F is the electric force, q1 and q2 are the charges, and r is the distance between them.
In this case, the charges are the -2.82uC charge and the point charges at x = 1.01m and x = -1.01m. The distance between them is the same as the value of r calculated earlier.
F1 = (k * q1 * q2) / r1^2
F2 = (k * q1 * q2) / r2^2
To find the net electric force, you need to add the forces due to both charges:
F_net = F1 + F2
By following these steps, you should be able to determine the electric field on the y-axis and calculate the electric force on the given charge. Make sure to double-check your calculations and any vector additions to identify any potential errors in your previous attempts.