Question

The insulating solid sphere in the previous Example 24.5 has the same total charge Q and radius a as the thin shell in the example here. Consider the electric fields due to the sphere (E_sphere), the shell (E_shell), and a point charge Q (E_Q). Rank the strength of the electric fields due to these three charged objects at the same three points ('1' represents the object with the strongest, '2' for the next in strength and so on. For example, you can have the triad {3, 1, 2} as your answer, or {2, 1, 2} if the shell is strongest while the sphere and the point charge have equal strengths.): r greaterthan a a. {1, 1, 2} b. {2, 1, 1} c. {1, 1, 1} d. {2, 2, 1} e. {1, 2, 3} r lesserthan a a. {2,2, 1} b. {1,1,1} c. {2, 3, 1} d. {2,1,1} e.{1, 2, 1}

Answer 1

Answer and Explanation:

Using Gauss's law,

If r>a

then charge enclosed in all the three cases is same as Q.

So Electric field for all three is same.

So {1,1,1}.

(b) r<a,

Charge enclosed in case of shell is zero since all charge is present on the surface. So E = 0.

Charge enclosed by incase of point charge is Q.

Charge enclosed in case of sphere is Qr3/a3 which is less than Q.

So ranking {2,3,1}