How Does an Electron Move in the Field of a Uniformly Charged Ring?

In summary, the conversation discusses the placement of an electron on the axis of a uniformly charged ring with a radius of 10.0cm and a total charge of +12.0nC. The question is how to determine the speed of the electron when it reaches the center of the ring. The conversation goes on to discuss using electric potential to find the potential energy at different distances along the axis and at the center of the ring. However, there is uncertainty about how to convert the charge from nC to C in the equation.
  • #1
defineNormal
10
0
ok here goes,

A uniformly charged ring has a radius equal to 10.0cm and a total charge of +12.0nC. An electron is placed on the ring's axis at a distance of 25.0cm from the center of the ring and is constrained to stay on the axis of the ring. The electron when it reaches the center of the ring?

ok so
Q=+12.0nC
r=0.10m
x=0.25m

here's what I got so far

dE=Ke*dq/r^2
r=(x^2+a^2)^(1/2)
<after integration>
=Ke^x/(x^2+a^2)^(3/2)
I can't figure out how to find Ke> Am I heading in the right direction?
 
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  • #2
I am not sure what the question is. Is it: "what is the speed of the electron when it passes through the centre of the ring"?

If so, try using electric potential. What is the potential energy at a distance d along the axis? What is the potential energy at the centre of the ring? What is the difference? That has to be the kinetic energy of the electron.

AM
 
  • #3
woops, determine speed :)
 
  • #4
Ok this is what I got Ke(Q/(x^2+a^2) <--- square root over the donominator.
Q= 12.0 nC
a= 25.0cm => 0.25m
r= 10.0cm => 0.10m

the answer given is 1.19x10^7, I keep getting 1.488x10^12, however I see where I wen't wrong because Ke=8.99x10^9 Nm^2/C^2, so this means I have to convert 12.0 nC to C, and I don't know how?
 
  • #5
defineNormal said:
Ok this is what I got Ke(Q/(x^2+a^2) <--- square root over the donominator.
Q= 12.0 nC
a= 25.0cm => 0.25m
r= 10.0cm => 0.10m

the answer given is 1.19x10^7, I keep getting 1.488x10^12, however I see where I wen't wrong because Ke=8.99x10^9 Nm^2/C^2, so this means I have to convert 12.0 nC to C, and I don't know how?

I assume if it really is nC it means nanoCoulombs or 10^-9C
 
  • #6
but then the exponants cancel each other out?
 
  • #7
defineNormal said:
but then the exponants cancel each other out?

Did you use the charge of the electron? Your equation below is not correct. The RHS is just K, not Ke

defineNormal said:
Ke=8.99x10^9 Nm^2/C^2

Other than that, check your computations. You appear to have the correct distances and the correct PE.
 

FAQ: How Does an Electron Move in the Field of a Uniformly Charged Ring?

1. What is the "Uniformly Charged Ring problem"?

The Uniformly Charged Ring problem is a common physics problem that involves calculating the electric field at a point on the axis of a charged ring with a uniform distribution of charge. It is used to demonstrate the principles of electrostatics and can be solved using the principles of Coulomb's law and the superposition principle.

2. How is the electric field calculated for a uniformly charged ring?

The electric field at a point on the axis of a uniformly charged ring can be calculated using the formula E = (kQx)/(R^2 + x^2)^(3/2), where k is the Coulomb constant, Q is the total charge of the ring, x is the distance from the center of the ring, and R is the radius of the ring.

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

The direction of the electric field for a uniformly charged ring is perpendicular to the plane of the ring and points away from the ring if the point is outside the ring, and towards the ring if the point is inside the ring. This can be determined using the principle of superposition and the direction of the electric field due to a point charge.

4. How does the electric field change as you move along the axis of a uniformly charged ring?

The electric field changes as you move along the axis of a uniformly charged ring because the distance from the point on the axis to different segments of the ring changes. As you move closer to the ring, the electric field increases, and as you move further away, the electric field decreases. The electric field also changes direction depending on whether the point is inside or outside the ring.

5. What are the real-life applications of the Uniformly Charged Ring problem?

The Uniformly Charged Ring problem has many real-life applications, such as calculating the electric field of a charged ring in a particle accelerator, calculating the electric field of a circular capacitor, and understanding the behavior of charged particles in a circular magnetic field. It is also used in engineering and design to optimize the placement and distribution of charges in different structures and devices.

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