Electric field from a circle arc

In summary, The x-component of the electric field at the origin due to the full arc length for a charge of 3.8 μC and a radius of 1.9 m is 12968.1 N/C. The method used was to calculate dq using the linear charge density, then use the formula for electric field to find the x-component by integrating from θ = 0 to π/2. This method was used because the Coulomb constant and the charge and radius values were given.
  • #1
nautola
16
0

Homework Statement


Find the x-component of the electric field
at the origin due to the full arc length
for a charge of 3.8 μC and a radius of
1.9 m. The value of the Coulomb constant
is 8.98755 × 109 N · m2/C2.


Homework Equations


E = kq/r^2
dq = q dθ
λ = Q/ (R θ)


The Attempt at a Solution


I said E = kq/r^2
And so Ex = kq/r2 * sinθ
and dEx = k*dq/r2 * sinθ
and dq = λ ds
ds = R dθ
λ = q/s
so dq = Q/θ dθ

I get kq/r2 ∫sinθ/ θ dθ

But when I input the answer from this integral (from the calculator) the answer is wrong.
 

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  • #2
What is your answer?
 
  • #3
I got 12968.1 N/C. Is my method correct?
 
  • #4
I don't think so.
dq = λ*ds, where
λ= q / s , ds = r*dθ and s = πr/2
Substituute these values in the expression of dE and find the integration taking limits θ = 0 to π/2
 
  • #5


I would like to clarify that the integral you have set up is incorrect. The correct integral should be kq/r^2 * ∫sinθ dθ, as the variable of integration is θ, not θ/θ. Additionally, the upper limit of integration should be the total arc length, not just θ. This will result in a correct value for the x-component of the electric field at the origin. It is important to carefully set up integrals and double check them to ensure accurate calculations.
 

1. What is the formula for calculating the electric field from a circle arc?

The formula for calculating the electric field from a circle arc is E = 2kQ/r, where E is the electric field, k is the Coulomb's constant, Q is the charge of the arc, and r is the distance from the center of the arc.

2. How does the angle of the circle arc affect the electric field?

The angle of the circle arc does not have a direct effect on the electric field. However, it does affect the distribution of the electric field, with a larger angle resulting in a more spread out field.

3. Can the electric field from a circle arc be negative?

Yes, the electric field from a circle arc can be negative. This occurs when the charge of the arc is negative or when the distance from the center of the arc is larger than the radius of the circle.

4. What is the direction of the electric field from a circle arc?

The direction of the electric field from a circle arc is radial, meaning it points away from the center of the arc. The direction can also be determined using the right-hand rule, where the fingers of your right hand curl in the direction of the electric field and your thumb points in the direction of the arc's curvature.

5. How does the radius of the circle arc impact the electric field?

The radius of the circle arc has an inverse relationship with the electric field. As the radius increases, the electric field decreases, and vice versa. This is because the larger the radius, the farther away the electric field is spread out, resulting in a weaker field.

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