Why is work infinite but potential energy zero for a charge near a grounded sphere?

[hokhani]

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?

 

[nasu]

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?

 

[hokhani]

it is the subject of one of the problems of jackson electrodynamics(problem5 chapter2)

 

[K^2]

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.

 

[Meir Achuz]

"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.

 

[hokhani]

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?

 

[Meir Achuz]

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.

 

[hokhani]

how can i acquire information aboat the grounded conducting?
please guide me.