Chapter 3 Department of Physics,HKU3章物理系，香港.pptVIP

* Chapter 3 Boundary-Value Problems In Electrostatics: One (3.1) Method of Images ? Method of images Real charges + Image charges Charges + induced charges Satisfy the same BC and Poission eq. The image charges must be external to the vol. of interest since inside the vol, Method of images:1) Same Poission eq. (charge distribution) inside Vol. 2) Same boundary conditions 3.2 Point charge in the presence of a grounded conducting sphere Question: Seek the potential V(r) in the case that a point charge q located at rq near a grounded conducting sphere with radius a. A grounded conducing sphere means that The potential due to the charge q and q’ We now try to find q’ and such that this potential satisfies . Original system Image system ---- a unit vector in the direction -- a unit vector in the direction Then we find the position and the magnitude of the image charge (1) The induced charge density Where g is the angle between and (2) The force between the sphere and q Method 1 Method 2 q da g The force between a point charge and its induced charges q A conducting plane Then the force on each element of area is given by 3.3 Point charge in the presence of a charged, insulated conducting sphere Start with the grounded conducting sphere (q’) disconnect the ground wire and add (Q-q’) Q 3.4 ?Point Charge Near a Conducting Sphere at Fixed Potential so long as the charge (Q-q’) on the surface is replaced by a charge V0 a 3.5 Conducting Sphere in a Uniform Electric Field A uniform can be thought of as being produced by appropriate position and negative charges at infinity. in a region near the origin whose dimensions are very small compared to R In the limit as constant, this approximation becomes exact. If now a conducting sphere of radius a is placed at the origin, the potential will be due to the charges