Understanding the Contradiction: Point Charge near Grounded Conducting Sphere

In summary, the potential energy at the surface of a neutral conducting sphere is zero. As soon as you place a charge in vicinity, it is no longer neutral, and the potential will depend on distance to the free charge. As that distance goes to zero, potential goes to -inf for the same reason as explained above. However, the potential energy for a point charge q a distance d from a grounded sphere of radius a is U=-aq^2/2(d-a). This --> -infty as a-->d. When we use the hmaginary charge theorem, we try select the imaginary charge so that the potential on the grounded conducting be zero as well as we take the potential equal to zero in the infinite.
  • #1
hokhani
506
8
suppose we have a point charge q near the grounded conducting sphere.
we know that the work down by electric field of the sphere for taking the point charge from surface of the sphere to infinite is infinit. but the potential energy in the grounded surface and infinite is zero.
what is the reson for this contradiction?
 
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  • #2
hokhani said:
suppose we have a point charge q near the grounded conducting sphere.
we know that the work down by electric field of the sphere for taking the point charge from surface of the sphere to infinite is infinit. but the potential energy in the grounded surface and infinite is zero.
what is the reson for this contradiction?

How do you know this?
 
  • #3
it is the subject of one of the problems of jackson electrodynamics(problem5 chapter2)
 
  • #4
nasu said:
How do you know this?
Because grounded conducting sphere creates a "reflection" of the charge, so the potential of a charge in contact with the sphere is -inf.

Potential at the surface of a neutral conducting sphere is zero. As soon as you place a charge in vicinity, it is no longer neutral, and the potential will depend on distance to the free charge. As that distance goes to zero, potential goes to -inf for the same reason as explained above.
 
  • #5
"but the potential energy in the grounded surface and infinite is zero."
No. The potential energy for a point charge q a distance d from a grounded sphere of radius a is U=-aq^2/2(d-a). This --> -infty as
a-->d.
 
  • #6
when we use the hmaginary charge theorem, we try select the imaginary charge so that the potential on the grounded conducting be zero as well as we take the potential equal to zero in the infinite. the work down by electric field for conveying the charge from infinite to surface is infinite.
is there anybody replying?
 
  • #7
You are confusing the potential on a grounded sphere with the potential energy of the configuration. We're going to stop replying if you can't understand this.
 
  • #8
how can i acquire information aboat the grounded conducting?
please guide me.
 

FAQ: Understanding the Contradiction: Point Charge near Grounded Conducting Sphere

What is the concept of a point charge near a grounded conducting sphere?

The concept of a point charge near a grounded conducting sphere refers to the behavior of an electrically charged particle in close proximity to a spherical object that is connected to the ground. This situation is often used as a model to study the behavior of electric fields and charges in a more complex system.

How does the presence of a grounded conducting sphere affect the electric field of a point charge?

The grounded conducting sphere acts as a shield, causing the electric field of the point charge to be distorted and redirected away from the sphere. This is due to the fact that the conducting sphere is able to redistribute the electric charge on its surface, creating an opposite electric field that cancels out the field of the point charge in the region close to the sphere.

What is the significance of understanding the contradiction between a point charge and a grounded conducting sphere?

Understanding the contradiction between a point charge and a grounded conducting sphere can help us to better understand the behavior of electric fields and charges in more complex systems. It also allows us to make predictions and calculations about the electric potential and energy in the vicinity of the sphere, which can have practical applications in fields such as electrical engineering and physics.

How can the contradiction between a point charge and a grounded conducting sphere be resolved?

The contradiction between a point charge and a grounded conducting sphere can be resolved by taking into account the effects of the conducting sphere on the electric field. This can be done through mathematical calculations or simulations, which can provide a more accurate understanding of the electric potential and energy in the system.

Are there any real-world applications of the concept of a point charge near a grounded conducting sphere?

Yes, there are several real-world applications of this concept. For example, it can be used to design and optimize electronic devices such as antennas, capacitors, and sensors. It can also be applied in the study of lightning strikes and the design of lightning protection systems. Additionally, it is relevant in the field of electrostatics, which has practical applications in industries such as printing, painting, and air purification.

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