Saved Bookmarks
| 1. |
A small metal sphere carrying charge +Q is located at the centre of a sphereical cavity inside a large uncharged metallic spherical shell. Use Gauss' law to find the expression for the electric field At a point P_1 situated inside the cavity at a distance x_1 from centre. (ii) At a point P_2 situated in the metalic spherical shell at a distance x_2from the centre. |
|
Answer» Solution :Let charge +Q is located at the centre O of a spherical cavity inside a large uncharged metallic spherical SHELL as shown in Then a charge -Q is induced on inner surface of shell and a charge +Q is induced on the outer surface of the shell. Let `P_1 ` be a point inside the cavity at a distance `x_1 ` from the centre O. To find ELECTRIC field ` E_1 ` at point `P_1`let us consider a spherical surface of radius `x_1` as the Gaussian surface. Then ,electric flus. ` phi _in =int oversetto E . oversetto (dS) =E_1 s_1 = E_1 (4 PI x_1^(2)) ` ` "" = (1)/( in_0) ("charge ENCLOSED")=(Q)/(in_0) ` ` RARR ""E_1 =(Q)/( 4 pi in _0 x_1^(2))` Let `P_2` be a point situated in the metallic shell at a distance `x_2` from the centre. To find electric field `E_2` at point ` P_2`let us again consider a spherical surface of radius `x_2` as the Gaussian surface. Then Electric flux ` "" phi_in =E_2s_2 =E_2 ( 4 pi x_2^(2))=(1)/( in _0)("charge enclosed") = (1)/( in_0)(Q-Q)= 0 ` `rArr""E_2 =0` 
|
|