InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
State Gauss theorem in electrostatics. Derive the expression for electric field at a point due to an infinitely long straight charged conductor. |
|
Answer» Solution :Statement: The total electric flux through a closed SURFACE in free space is equal to `(1)/(epsi_0) `times the net charge enclosed by the surface. `phi = (q)/( epsi_0)` Derivation :  In the above fig. AB is the infinitely long WIRE E is the electric field P is a point at a distance r from the wire . r. is the radius of GAUSSIAN cylinder .l is the length of the Gaussian cylinder Let .q. be the charge enclosed by the Gaussian cylinder. Let .`lamda `. be the linear charge density on the wire. Flux through the end faces is zero because there are no components of electric field ALONG the normal to the end faces. `phi = ` flux tħrough curved surface `phi = E xx `area of curved surface `(phi =E xx` area) `phi= E xx2pi rl to(1)` From Gauss.s theorem `phi =(q)/(epsi_0) to (2)` but ` lamda= (q)/(I)= q= lamda I` `(2)= phi =(lamda I)/( epsi_0 )to( 3) ` On comparing (1) and (3), we get `E xx 2 pi rI=(lamda I )/( epsi_0)` ` E= ( lamda )/(2 pi r epsi_0)` ` E=(1)/( 2 pi r epsi_0 )(lamda )/(r)` The direction of .E. is perpendicular to the wire and directed away from the wire. |
|