Three identical charges
(q =4.3 µC)lie along a circle of radius 1.9 m at angles of 30°, 150°, and 270°, as shown in the figure below. What is the electric field at the center of the circle?
I THOUGHT IT WOULD BE ZERO BUT MY PROF TELLS ME THAT'S WRONG WHY?
Sure looks like zero to me.
2 sin 30 = 1
To determine the electric field at the center of the circle, we need to consider the electric field contributions from each of the three charges. The formula for the electric field due to a point charge is given by:
E = k * (q / r^2)
Where:
- E is the electric field
- k is Coulomb's constant (k = 8.99 x 10^9 N m^2/C^2)
- q is the charge
- r is the distance between the charge and the point where we want to find the electric field
First, let's consider the charge located at 30°. The distance from this charge to the center is equal to the radius of the circle, which is 1.9 m. The electric field due to this charge at the center is:
E₁ = k * (q / r^2) = (8.99 x 10^9 N m^2/C^2) * (4.3 x 10^(-6) C) / (1.9 m)^2
Next, let's consider the charge located at 150°. The distance from this charge to the center is also equal to the radius of the circle, which is 1.9 m. The electric field due to this charge at the center is:
E₂ = k * (q / r^2) = (8.99 x 10^9 N m^2/C^2) * (4.3 x 10^(-6) C) / (1.9 m)^2
Finally, let's consider the charge located at 270°. The distance from this charge to the center is also equal to the radius of the circle, which is 1.9 m. The electric field due to this charge at the center is:
E₃ = k * (q / r^2) = (8.99 x 10^9 N m^2/C^2) * (4.3 x 10^(-6) C) / (1.9 m)^2
Now, since the charges are evenly spaced around the circle, they will contribute equally to the electric field at the center. This means we can simply sum up the electric field contributions from each charge to get the total electric field at the center:
E_total = E₁ + E₂ + E₃
Substituting the calculated values in the equations, we can find the total electric field.