Finding the Mirror Image Charge for a Point Charge Near a Conducting Sphere

Click For Summary
SUMMARY

The discussion focuses on calculating the mirror image charge for a point charge Q located outside a grounded conducting sphere of radius a. The point charge induces an opposite charge on the sphere, creating an electric field equivalent to that produced by the point charge and a fictional image charge q. The image charge q must be positioned along the axis connecting the center of the sphere and the point charge Q, ensuring that the sphere's surface remains an equipotential at zero potential. The method of images is the key technique for solving this problem.

PREREQUISITES
  • Understanding of electrostatics and electric fields
  • Familiarity with the method of images in electrostatics
  • Knowledge of grounded conductors and their behavior in electric fields
  • Basic principles of Gauss' Law
NEXT STEPS
  • Study the method of images in electrostatics
  • Review the principles of grounded conductors and their charge distribution
  • Learn how to apply Gauss' Law to various charge configurations
  • Explore problems involving point charges and conducting surfaces
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone studying electrostatics, particularly those interested in the behavior of charges near conductive materials.

Bloodplasma
Messages
2
Reaction score
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
Mate, it's about Gauss' Law. Haven't you got any books?
 
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.
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
1K
Replies
7
Views
4K
  • · Replies 2 ·
Replies
2
Views
5K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
3
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 49 ·
2
Replies
49
Views
7K
Replies
12
Views
2K