Electric field due to a distributed charge over a ring

In summary: So no, it should not be (0.4i^ + 0.025j^)/(r).In summary, a ring-shaped conductor with a radius of 0.025 m and a total positive charge of 0.125 x 10-9C uniformly distributed around it has an electric field at a specific point on the x-axis at x = 0.4m. By using the given equations and attempting to solve for the electric field, it was discovered that the value for ##\hat{r}## may be incorrect as the electric field in the y-direction was not equal to 0. Upon reevaluation, it was determined that ##\hat{r}## will have varying y and z components and
  • #1
henry3369
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Homework Statement


.A ring-shaped conductor with radius a = 0.025 m has a total positive charge Q = 0.125 x 10-9C uniformly distributed around it. The center of the ring is at the origin of coordinates O.

What is the electric field (magnitude and direction) at point , which is on the x-axis at x = 0.4m.

Homework Equations


dq = λ(ds)
Q = λ(2πr)
dE = ((k)(dq)/r2) * (r^)

The Attempt at a Solution


So I figured out how to solve the electric field using the equations above, but for some reason I am not getting 0 for the electric field in the y-direction. I know that it has to be zero because all the electric fields cancel out in the vertical direction so I'm assuming my value for r^ is incorrect. Is it supposed to be (0.4i^ + 0.025j^)/(r)? It seems like it should be ((0.4i^ + 0j^)/(r) in order to get 0 for the vertical direction. After solving I end up with E = (6.98i^ + 0.4364j^) and the electric field in the x-direction is correct, but I don't think there is supposed to be a field in the y-direction. So, can someone tell me if my value for r^ is correct?
 
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  • #2
henry3369 said:
... so I'm assuming my value for r^ is incorrect. Is it supposed to be (0.4i^ + 0.025j^)/(r)?
By drawing a figure you should see that ##\hat{r}## will have y and z components that vary as you integrate over the ring.
 
Last edited:

1. What is an electric field due to a distributed charge over a ring?

The electric field due to a distributed charge over a ring is the force per unit charge at any point in space surrounding the ring. It is a vector quantity that describes the strength and direction of the electric force experienced by a unit positive charge at a given point.

2. How is the electric field calculated for a distributed charge over a ring?

The electric field due to a distributed charge over a ring can be calculated using Coulomb's law, which states that the electric field at a point is equal to the sum of the electric fields from each individual charge in the ring. This can be expressed mathematically as E = kq/r2, where k is the Coulomb's constant, q is the charge, and r is the distance from the charge to the point where the electric field is being calculated.

3. How does the electric field change as the distance from the ring increases?

As the distance from the ring increases, the electric field decreases according to an inverse square law. This means that the electric field is inversely proportional to the square of the distance from the ring. This relationship can be seen in the equation for the electric field, where the electric field decreases as the distance (r) increases.

4. What factors affect the strength of the electric field due to a distributed charge over a ring?

The strength of the electric field due to a distributed charge over a ring is affected by the amount of charge distributed on the ring, the distance from the ring, and the shape of the ring. The electric field is stronger when there is more charge, closer to the ring, and when the ring is larger in size.

5. How is the direction of the electric field determined for a distributed charge over a ring?

The direction of the electric field can be determined using the principle of superposition. The electric field at a point is the vector sum of the electric fields from each individual charge in the ring. The direction of the electric field is always perpendicular to the ring at any given point and points away from the ring for positive charges and towards the ring for negative charges.

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