A small conducting spherical shell with inner radius `a` and outer radius `b` is concentric with a larger conducting spherical shell with inner radius `c` and outer radius `d` ( as shown in Fig . 2.121). The inner shell has a total charge ` + 2 q`, and the outer shell has a total charge ` + 4 q`. Calculate the electric field in terms of `q` and the distance `r` from the common center of the two shells for

`r lt a`

Options

A. zero
B. `(1)/( 4 pi epsilon_(0)) ( 2q)/( r^(2))`
C. `-(1)/(4 pi epsilon_(0)) ( 6 q)/( r^(2))`
D. `(1)/( 4 pi epsilon_(0)) (q)/( r^(2))`

Answer

A

Explanation

i. `r lt a. E = 0 `, since `Q = 0` ( fig.S2.54)
ii. `a lt r lt b. E = 0` , since `Q = 0` .
iii. `b lt r lt c`. Since `Q = + 2 q , E = (1)/( 4 pi epsilon_(0)) ( 2q)/(r^(2))`
iv. C lt r lt d. E = 0 , since `Q = 0`.
v. r gt d. E = (1)/( 4 pi epsilon_(0)) ( 6 q)/( r^(2))` , since `Q = + 6 q`.