# Electric Field of a Uniformly Charged Ring

• ILoveCollege
In summary, a uniformly charged ring with a radius of 8.1 cm and a total charge of 118 micro Coulombs is given. Using the Coulomb constant of 8.98755e9 N M^2/C^2, the magnitude of the electric field on the axis of the ring at 1.15 cm from the center is being asked for. The equations used to solve this are F= k Qq/ r^2 and E= kq/r^2, and the solution involves finding the value of "r" using the Pythagorean theorem. However, it is unclear whether the axis being referred to is horizontal or vertical.

## Homework Statement

A uniformly charged ring of radius 8.1 cm has a total charge of 118 micro Coulombs. The value of the Coulomb constant is 8.98755e9 N M^2/C^2. Find the magnitude of the electric field on the axis of the ring at 1.15 cm from the center of the ring. Answer in units of N/C.

F= k Qq/ r^2
E= kq/r^2

## The Attempt at a Solution

I tried subtracting 1.15 cm from 8.1 cm for "r" and plugged that "r" value in the F equation but that answer is wrong. By axis , do they mean horizontally (as in along the diameter) or vertically?

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do i just do the pyth. theorem to solve for "r" ( square root of 8.1^2 + 1.15^2)?

I would first clarify with the person who provided this problem what they mean by "axis." This term can be interpreted in different ways, and it is important to have a clear understanding in order to solve the problem correctly.

Assuming that "axis" refers to the horizontal axis (along the diameter) of the ring, I would approach the problem by first calculating the linear charge density of the ring, which is the total charge divided by the circumference of the ring. This would give us the charge per unit length.

Next, I would use the formula for the electric field due to a charged ring, which is E = kλx / (x^2 + R^2)^3/2, where λ is the linear charge density, x is the distance from the center of the ring, and R is the radius of the ring.

Plugging in the given values, we can calculate the electric field at 1.15 cm from the center of the ring. Be sure to convert all units to SI units before plugging in to the formula.

If "axis" refers to the vertical axis, the approach would be similar, but using the formula for the electric field due to a charged disk instead. This formula is E = kσz / (z^2 + R^2)^3/2, where σ is the surface charge density, z is the distance from the center of the disk, and R is the radius of the disk.

Again, I would clarify with the person who provided the problem to ensure that the correct formula is being used.

## 1. What is the formula for the electric field of a uniformly charged ring?

The formula for the electric field of a uniformly charged ring is E = kQz/(z^2 + R^2)^(3/2), where k is the Coulomb constant, Q is the total charge of the ring, z is the distance from the center of the ring, and R is the radius of the ring.

## 2. How does the electric field change as you move away from the center of the ring?

The electric field decreases as you move away from the center of the ring. This is because the electric field is inversely proportional to the distance from the center of the ring.

## 3. Is the electric field inside the ring zero?

Yes, the electric field inside the ring is zero. This is because the electric field is only present on the outside of the ring and cancels out on the inside due to the symmetrical distribution of charge.

## 4. Can the electric field of a uniformly charged ring be negative?

Yes, the electric field of a uniformly charged ring can be negative. This can occur if the distance from the center of the ring is greater than the radius, causing the numerator of the formula to be negative.

## 5. How does the electric field of a uniformly charged ring compare to that of a point charge?

The electric field of a uniformly charged ring is different from that of a point charge. While the electric field of a point charge decreases as the inverse square of the distance, the electric field of a uniformly charged ring decreases as the inverse cube of the distance. Additionally, the electric field of a uniformly charged ring is zero inside the ring, while the electric field of a point charge is non-zero at all points.