Ring of charge, Variation of V and E

In summary, a thin ring of radius x with a uniformly distributed charge Q will have a potential and electric field that vary along the axis. The potential will be highest at the center and decrease as you move away, while the electric field will be strongest at the edges and decrease towards the center. A dipole placed at the center of the ring will experience no net force due to the symmetric nature of the potential and electric field along the axis.
  • #1
kmoukiss
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0

Homework Statement



A thin ring of radius x carries a charge Q uniformly distributed around it.
Sketch garphs showing how the potential and the field vary along the axis (y) from its centre.
A small dipole of strength p is placed at the centre of the ring so as to point alonf th axix (going through the centre, so vertical). What force does the ring exert on the dipole?


Homework Equations



I had to first find the expression for the potential and the electric field.

The Attempt at a Solution



For the sketch, I am a bit struggling... shall I think about it as for a point charge ?
For the dipole, I think there is no force on it because all the components cancel out...

Thank you for helping me !
 
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  • #2




Thank you for your question. To sketch the graphs, you can start by considering the potential and electric field of a point charge, as you mentioned. However, keep in mind that for a ring, the potential and electric field will vary along the y-axis due to the distribution of charge around the ring.

The potential along the axis will be highest at the center of the ring and decrease as you move away from the center. It will also be symmetric about the center of the ring. The electric field, on the other hand, will be strongest at the edges of the ring and decrease towards the center.

As for the dipole, you are correct in thinking that the force on it will be zero. This is because the field from the ring will be uniform along the axis, and the dipole will experience equal and opposite forces from the positive and negative charges on the ring, resulting in a net force of zero.

I hope this helps. Good luck with your work!
 

1. What is a ring of charge?

A ring of charge is a theoretical model used in physics to represent a circular distribution of electric charge. It is often used to study the behavior of electric fields and potential in a two-dimensional system.

2. How does the electric potential (V) vary around a ring of charge?

The electric potential (V) around a ring of charge varies according to the inverse relationship of the distance from the ring. This means that as you move closer to the ring, the potential increases, and as you move further away, the potential decreases.

3. What is the relationship between the electric potential and the electric field (E) around a ring of charge?

The electric field (E) around a ring of charge is directly proportional to the rate of change of the electric potential (V). This means that where the electric potential is changing rapidly, the electric field will be stronger, and where the potential is changing slowly, the electric field will be weaker.

4. How do the electric potential and electric field vary with distance from the center of a ring of charge?

The electric potential (V) and electric field (E) around a ring of charge vary inversely with the distance from the center of the ring. This means that as you move further away from the center, the potential and field will decrease.

5. What is the significance of studying the ring of charge and its variation of V and E?

Studying the ring of charge and its variation of V and E allows scientists to understand and predict the behavior of electric fields and potential in a two-dimensional system. This is important in various fields such as electromagnetism, electronics, and particle physics.

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