Ring of charge electric potential

In summary, the conversation discusses finding the potential difference at a point D perpendicular to the center of a ring in the z,y plane. The given variables are D, R, Q, X, λ, dX, and dQ, and the relevant equation is \int \frac{kλrdθ}{(D^2+R^2)^{1/2}}. The question is how to integrate this expression to find the potential difference. The solution is to integrate from 0 to 2pi with θ as the variable of integration.
  • #1
Panphobia
435
13

Homework Statement


The ring is in the z,y plane.
D = 2m
R = 4m
Q = 8 * 10^-6 C
X = distance to the edge
λ = dQ/dX
dX = rdθ
dQ = infinitely small charge
dX = infinitely small arc of ring

What is the potential difference at the point D perpendicular to the centre of the ring?

Homework Equations


[itex]\int \frac{kdQ}{X}[/itex]

The Attempt at a Solution



[itex]\int \frac{kλrdθ}{(D^2+R^2)^{1/2}}[/itex]
After this how do I get it in terms of dθ?
 
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  • #2
What is the question ? Are you required to find the potential of the ring at a point 2m away from the center ,and lying on the axis of the ring ?
 
  • #3
Yea I gave the question after all the variables were specified
 
  • #4
What is the problem ? Just integrate the expression with appropriate limits.The variable of integration is θ .
 
  • #5
Thats it?
 
  • #6
Panphobia said:
Thats it?

What does that mean ?
 
  • #7
So what are we integrating to 0 to 2pi?
 
  • #8
Yes... the range of θ is 0 to 2pi .
 

What is the "Ring of charge electric potential"?

The "Ring of charge electric potential" refers to the electric potential created by a ring of charge, which is a hypothetical scenario in which a ring-shaped object is uniformly charged with a certain amount of electric charge.

How is the electric potential of a ring of charge calculated?

The electric potential of a ring of charge can be calculated using the equation V = kQ/r, where V is the electric potential, k is the Coulomb's constant, Q is the charge on the ring, and r is the distance from the center of the ring to the point at which the electric potential is being measured.

What is the difference between electric potential and electric field?

Electric potential and electric field are closely related, but they are not the same thing. Electric potential is a scalar quantity that relates to the amount of work required to move a unit of charge from one point to another, while electric field is a vector quantity that describes the force experienced by a unit of charge at a specific point in space.

How does the electric potential of a ring of charge change with distance?

The electric potential of a ring of charge decreases as the distance from the center of the ring increases. This is because the electric potential is inversely proportional to the distance from the center of the ring, according to the equation V = kQ/r.

What are some real-life applications of the concept of "Ring of charge electric potential"?

The concept of "Ring of charge electric potential" has various applications in fields such as electrostatics, electromagnetism, and particle physics. It is used to understand and predict the behavior of charged particles in electric fields, as well as in the design of technologies such as particle accelerators and capacitors.

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