Point Charge around a sphere

In summary, a point charge outside a grounded conducting sphere will create a charge on the sphere that will result in an attractive force towards the sphere. The electric field outside the sphere can be calculated using the method of images, which involves adding a fictional "image charge" to the actual charge on the sphere. The value and location of the image charge can be determined using symmetry and the axis passing through the center of the sphere and the location of the point charge. This method can be found in textbooks.
  • #1
Bloodplasma
2
0

Homework Statement



A point Charge Q is placed a distance R from the center of a conducting sphere of radius a, with R>a, i.e. the point charge is outside the sphere. The sphere is grounded- connected to a distant, unlimited source/sink of charge at zero potential. (Neither the distant "ground" nor the connection directly affects the electric field in the vicinity of the charge and sphere.) As a result, the sphere acquires a charge opposite in charge to Q, and the point charge experiences an attractive force toward the sphere.

Remarkably, the electric field outside the sphere is the same as would be produced by the given point charge Q plus a mirror image point charge q, of such value and location as to make the set of point corresponding to the surface of the sphere an equipotential of potential zero. That is, the fictional "image charge" gives the same field contribution outside the sphere as the actual surface charge on the sphere. Calculate the value and location of charge q. HINT: By symmetry, charge q must lie somewhere on the axis which passes through the center of the sphere and the location of charge Q.

Homework Equations




The Attempt at a Solution



I am assuming its a solid sphere of uniform density, other then that i am not sure how to go about solving this.
 
Physics news on Phys.org
  • #2
Mate, it's about Gauss' Law. Haven't you got any books?
 
  • #3
Phred101.2 said:
Mate, it's about Gauss' Law. Haven't you got any books?
It's not Gauss, but the method of images, which should be described in your textbook.
 

1. What is a point charge?

A point charge is a theoretical concept in physics that represents a single, isolated electric charge at a specific location in space. It is considered to have no physical size and is usually represented by the symbol "q".

2. How does a point charge interact with a sphere?

A point charge placed near or around a conducting sphere will create an electric field that will cause the charges within the sphere to redistribute. This redistribution will cause the sphere to become polarized, with the opposite charges being attracted to the point charge and the like charges being repelled.

3. What is the equation for the electric field of a point charge around a conducting sphere?

The electric field of a point charge around a conducting sphere can be calculated using the equation E = kq/r2, where k is the Coulomb's constant, q is the charge of the point charge, and r is the distance between the point charge and the center of the sphere.

4. How does the electric field vary with distance in a point charge-sphere system?

The electric field around a point charge-sphere system follows an inverse square law. This means that as the distance from the point charge increases, the electric field decreases at a rate proportional to the inverse of the square of the distance.

5. Can a point charge be placed inside a conducting sphere?

No, a point charge cannot be placed inside a conducting sphere because the electric field produced by the point charge would cause the charges within the sphere to redistribute and cancel out the electric field inside the sphere. This means that the electric field inside the sphere would be zero, and the point charge would not experience any force.

Similar threads

  • Advanced Physics Homework Help
Replies
7
Views
2K
  • Advanced Physics Homework Help
Replies
2
Views
2K
  • Advanced Physics Homework Help
Replies
3
Views
399
  • Introductory Physics Homework Help
Replies
17
Views
325
  • Advanced Physics Homework Help
Replies
4
Views
2K
  • Advanced Physics Homework Help
2
Replies
49
Views
4K
  • Advanced Physics Homework Help
Replies
16
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
3
Views
1K
  • Advanced Physics Homework Help
Replies
4
Views
2K
Back
Top