Question

Place the following list of scenarios in order from greatest energy required to least energy required, and explain using physics why you chose that order: i) A charge +q is brought in from ∞ to a distance r from a conducting sphere holding charge +Q; ii) A charge +q is brought in from ∞ to a distance r/2 from a conducting sphere holding charge +Q; iii) A charge +q is brought in from ∞ to a distance r from a conducting sphere holding charge +2Q; iv) A charge +q is brought in from ∞ to a distance r from a conducting sphere holding charge −Q; v) A charge +q is brought in from ∞ to an equidistance r from a conducting sphere of charge +Q and another sphere of charge −Q.

Answer 1

Since the point of consideration is outside the point we can consider the sphere as a point charge.

The potential energy of the system consisting of two point charges (say q₁ and q₂) is :

kq2/r

a). The difference in potential energy

0-kqQ/rkqQ/r
, therefore the work done = -(The difference in potential energy ) =  
(-kqQ/r) kqQ/r

b). The difference in potential energy

0-kqQ/(r/2)-kqQ[(r/2)

therefore the work done = -(The difference in potential energy ) =  

-kqQ/(r/2)) 2kqQ/r

c). The difference in potential energy

,

0 kq2Q/r=kq2Q/r

therefore the work done = -(The difference in potential energy ) =  

-kq2Q/r) kq2Q/r

d). The difference in potential energy

,

therefore the work done = -(The difference in potential energy ) =  

(-kq(-Q)/r) kq(-Q)/

e).The difference in potential energy

,

therefore the work done = -(The difference in potential energy ) =  $-0=0$

Decreasing order :

b= c >a > e> d