Question : A small sphere of radius r1 and charge q1 is enclosed by a spherical shell of radius r2 and charge q2. Show that if q1 is positive, charge will necessarily flow from the sphere to the shell (when the two are connected by a wire), no matter what the charge q2 on the shell is.
Doubt by Riddhi
Solution :
Electric Potential at any point on the surface of Charged spherical shell
V1=kq2/r2 + kq1/r2
V1=kq2/r2 + kq1/r2
Electric Potential at any point on the surface of small sphere
V2=kq1/r1+kq2/r2
Potential difference between the small sphere and the shell
V2-V1
=kq1/r1+kq2/r2 - [kq2/r2 + kq1/r2]
V2=kq1/r1+kq2/r2
Potential difference between the small sphere and the shell
V2-V1
=kq1/r1+kq2/r2 - [kq2/r2 + kq1/r2]
=kq1/r1+kq2/r2-kq2/r2-kq1/r2
=kq1/r1-kq1/r2
=kq1[1/r1-1/r2]
Clearly the potential difference between the small sphere and shell is independent of either the magnitude or polarity of the charge q2.
=kq1/r1-kq1/r2
=kq1[1/r1-1/r2]
Clearly the potential difference between the small sphere and shell is independent of either the magnitude or polarity of the charge q2.
If q1 is positive then V2 [Potential on Small Sphere] is greater than the V1 [Potential on the shell] and hence the charge will necessarily flow from the sphere to the shell (when the two are connected by a wire), no matter what the charge q2 on the shell is.
Similar Question : Can ever the whole excess charge of a body P be transferred to the other Q ? If yes, how and if not, why?
Similar Question : Can ever the whole excess charge of a body P be transferred to the other Q ? If yes, how and if not, why?
Solution : Yes, the whole charge of a body P can be transferred to a conducting body Q, when P is enclosed by Q and is connected to it. This is because the charge always resides on the outer surface of the conductor.
