Electric Field of Uniformly Charged Ring

In summary, the electric field on the axis of a uniformly charged ring of radius 10.0 cm and total charge of 58.0μC can be calculated using the formula E= (kQx)/(x^2+r^2)^(3/2), where x is the distance from the center of the ring and r is the radius. This formula is derived through integration, taking into account the contributions of tiny pieces of the ring as individual point charges. This is explained in more detail in calculus-based physics textbooks.
  • #1
bowdish.9
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A uniformly charged ring of radius 10.0 cm has a total charge of 58.0μC. Find the electric field on the axis of the ring at the following distances from the center of the ring. (Choose the x-axis to point along the axis of the ring.).

I know the equation I want to use is E= (kQx)/(x^2+r^2)^(3/2)
where x is distance from the center of the ring and r is the radius.

But, I don't know where this equation comes from. I know E=kq/r^2, so I'm just not sure where the x/(x^2+r^2)^(3/2) comes from.
 
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  • #3
The formula that you wrote: E = kq/r^2, is the field of a point charge. If you have a ring of charge, you have to calculate the field due to tiny pieces of the ring, each considered a point charge, and vectorially add the fields. This process, in the limit as each tiny piece tends to zero size, is called integration. If you do the integration, you will get the more complicated formula that you wrote. This is given in detail in any calculus based textbook of introductory physics
 

1. What is an electric field?

An electric field is a physical quantity that describes the influence of electric charges on other charges in their vicinity. It is a vector quantity, meaning it has both magnitude and direction, and is measured in units of newtons per coulomb (N/C).

2. What is a uniformly charged ring?

A uniformly charged ring is a hypothetical ring with a constant distribution of electric charge along its circumference. This means that the charge is evenly spread out around the entire ring.

3. How is the electric field of a uniformly charged ring calculated?

The electric field of a uniformly charged ring can be calculated using the equation E = (kQz)/(R2 + z2)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 to the point where the electric field is being measured, and R is the radius of the ring.

4. What is the direction of the electric field of a uniformly charged ring?

The electric field of a uniformly charged ring points radially outward from the center of the ring. This means that if you were to place a positive test charge at any point around the ring, it would feel a repulsive force away from the center of the ring.

5. How does the electric field of a uniformly charged ring vary with distance?

The electric field of a uniformly charged ring follows an inverse square law, meaning that as the distance from the ring increases, the strength of the electric field decreases. This can be seen in the equation E = (kQ)/(r2), where r is the distance from the center of the ring. As r increases, the denominator becomes larger, resulting in a smaller electric field.

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