A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting sphereical shell with inner radius c and outer radius d. The inner shell has total charge `+2q` and the outer shell has charge `+4q`.
a. Make a plot of the magnitude of the electric field versus r.
b. Calculate the electric field `("magnitude and direction in terms of q")` and the distance r from the common centre of the two shell for `(i) rlta, (ii)altrltb, (iii) `bltrltc,` (iv) `cltrltd`, (v) `rgtd`. Show uour result in a graph with radial component of `vecE` as function of `r`.
c. What is the total charge on the
i. inner surface of the small shell,
ii. outer surface of the small shell,
iii. inner surface of the large shell,
iv. outer surface of the large shell?

Explanation

b. i,ii. For rltb, electric field is zero, because there is no charge inside.
iii. For `cgtrgt`b, electric field will be similar to that as if a point charge `2q` is placed at the centre.
iv. For `dgtrgtc`, electric field will be zero, as there is no charge inside.
v. For `rgtd`, electric field will be similar to that as if a point charge `6q` is placed at the centre.
The resulting plot is as shown in figure

c. i.0
ii. `+2q`
iii.` -2q`
iv. `+6q`.