Charged ring inside a conducting sphere.

In summary, a charged ring inside a conducting sphere refers to a scenario where an electrically charged ring is placed inside a hollow conducting sphere. The charges on the ring induce opposite charges on the inner surface of the sphere, creating an electric field inside the sphere and causing the charges on the ring to redistribute. As the ring is moved inside the sphere, the charge distribution changes and can be neutralized by adjusting the initial charge and properties of the sphere. This setup has practical applications in the construction of capacitors and in the study of electrostatics.
  • #1
A thin charged (charge=Q) ring of radius a centered on the z axis lies in the x-y plane. The potential outside the ring is given. Now the ring is placed inside a grounded conducting spherical shell of radius b > a. What is the potential inside the ring and between the ring and the sphere. I'd like to solve this problem without using the method of images. Any thoughts? Thanks
 
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  • #2
calcisforlovers said:
Any thoughts? Thanks

post in the homework forum.
 
  • #3


This is an interesting problem in electrostatics. Without using the method of images, we can approach this problem by considering the properties of a conducting sphere and the principle of superposition.

First, let's consider the potential inside the ring. Since the conducting sphere is grounded, its potential is zero. This means that the potential inside the ring must also be zero, as the sphere shields the electric field from the ring.

Next, let's consider the potential between the ring and the sphere. We can use the principle of superposition to calculate the potential at any point between the ring and the sphere. This means we can break down the problem into two parts: the potential due to the ring alone and the potential due to the sphere alone.

The potential due to the ring can be calculated using the given potential outside the ring. We can use the equation for the potential of a ring, V = Q/(4πε0r), where r is the distance from the center of the ring. Since the ring is centered on the z-axis, the potential will only depend on the distance from the z-axis. This means that the potential due to the ring will have the same form as the given potential outside the ring, but with a different constant.

Now, we can consider the potential due to the spherical shell. The potential inside a grounded conducting sphere is constant and equal to the potential at its surface. This means that the potential inside the sphere will be equal to the potential at the surface of the sphere, which is given to be V = Q/(4πε0b).

Using the principle of superposition, we can add these two potentials to find the total potential between the ring and the sphere. This will give us the following equation:

V = Vring + Vsphere = Q/(4πε0r) + Q/(4πε0b)

We can simplify this equation to get:

V = Q/(4πε0)(1/r + 1/b)

This is the potential between the ring and the sphere without using the method of images.

In conclusion, by considering the properties of a conducting sphere and using the principle of superposition, we can calculate the potential inside the ring and between the ring and the sphere without using the method of images. This approach allows us to solve the problem in a straightforward manner and gain a better understanding of the behavior of electric fields in this system.
 

1. What is a charged ring inside a conducting sphere?

A charged ring inside a conducting sphere refers to a scenario where an electrically charged ring is placed inside a hollow conducting sphere. The ring and the sphere are both made of conductive materials, allowing for the transfer of electric charge.

2. What happens when a charged ring is placed inside a conducting sphere?

When a charged ring is placed inside a conducting sphere, the charge on the ring induces opposite charges on the inner surface of the sphere. This creates an electric field inside the sphere, which causes the charges on the ring to redistribute. The final distribution of charges depends on the initial charge on the ring and the properties of the conducting sphere.

3. How does the charge distribution change as the ring is moved inside the sphere?

As the charged ring is moved inside the conducting sphere, the induced charges on the inner surface of the sphere will also move. This causes the electric field inside the sphere to change, which in turn affects the distribution of charges on the ring. The final distribution of charges will depend on the position of the ring inside the sphere.

4. Can the charge on the ring be neutralized inside the conducting sphere?

Yes, the charge on the ring can be neutralized inside the conducting sphere. This can be achieved by adjusting the initial charge on the ring and the properties of the conducting sphere. When the charge on the ring is neutralized, the electric field inside the sphere will be zero and the charges on the ring will redistribute accordingly.

5. What are the practical applications of a charged ring inside a conducting sphere?

One practical application of a charged ring inside a conducting sphere is in the construction of capacitors. The conducting sphere acts as one plate of the capacitor, while the charged ring acts as the other plate. This configuration allows for the storage and release of electrical energy. Another application is in the study of electrostatics and electric fields, as this scenario helps to demonstrate the concept of induced charges and electric field lines.

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