Given, ratio of radii of two metal sphere, R1:R2=4:7
R1
R2
=
4
7
If q1 and q2 be the charges on both the spheres after being contact with charge of 8.8×10−7C. then q1+q2=8.8×10−7C=0.88µC ⇒q1+q2=0.88µC If V be the common potential on both the spheres after connection, then q1=C1V and q2=C2V ∴
q1
q2
=
C1V
C2V
=
C1
C2
=
4πε0R1
4πε0R2
⇒
q1
q2
=
R1
R2
=
4
7
⇒q1=
4
7
q2 ......(ii) From Eqs. (i) and (ii), we get
4
7
q2+q2=0.88 ⇒q2=
7
11
×0.88=0.56µC ∴q1=0.88−q1=0.88−0.56=0.32µC i.e charge on smaller sphere, q1=0.32×10−6C ∴ Potential due to smaller sphere at r=60m
