Question

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. The inner shell has a total charge of -1q and the outer shell has a total charge of +3q.

Select True or False for the following statements.

1. The total charge on the inner surface of the small shell is -4q.

2. The total charge on the outer surface of the small shell is zero.

3. The total charge on the inner surface of the large shell is +1q.

4. The radial component of the electric field in the region c < r < d is given by +3q/(4πε0r2).

5. The total charge on the outer surface of the large shell is +2q.

6. The radial component of the electric field in the region r > d is given by +2q/(4πε0r2).

7. The radial component of the electric field in the region r < a is given by +2q/(4πε0r2).

Answer 1

The total charge on the inner surface of the small shell is -4q.

False, there is no charge enclosed inside the small shell

---------------------------------

The total charge on the outer surface of the small shell is zero.

False. The charge -1q will reside on the outer surface of the small shell

----------------------------------------

The total charge on the inner surface of the large shell is +1q.

Q (inner surface of small shell) + Q ( outer surface of small shell) + Q ( inner surface of large shell) = 0

0 - 1q + Q ( inner surface of large shell) = 0

Q ( inner surface of large shell) = + 1q

so, it is true

------------------------------------------------

The radial component of the electric field in the region c < r < d is given by +3q/(4πε0r2).

False - no charge is enclosed, so E = 0

---------------------------------------------------

The total charge on the outer surface of the large shell is +2q

Q = Q ( inner surface of large shell) + Q ( outer surface of large shell)

+ 3q = + 1q +  Q ( outer surface of large shell)

Q ( outer surface of large shell) = + 2q

so,

it is True

-------------------------------------------------------

The radial component of the electric field in the region r > d is given by +2q/(4πε0r2).

True

-------------------------------------------------

The radial component of the electric field in the region r < a is given by +2q/(4πε0r2).

False, as q = 0, so. E = 0