A solid conducting sphere of radius r = 1 cm is embedded at the boundary between a dielectric and air such that half of the sphere is in the dielectric and half is in the air. This conguration is shown in cross-section in the accompanying gure. The total charge on the sphere is 1 nC.
![Question 3 15 marks]: A solid conducting sphere of radius r 1cm is embedded at the boundary between a dielectric and air such](http://img.homeworklib.com/images/fb308851-9c33-4103-af70-4d45aeefd91e.png?x-oss-process=image/resize,w_560)
Homework Answers
Solution:
Given data in question,
Sphere radius r=1cm
Total charge Q=1nc
Electric potential formula:-
Potential at a point due to a fixed charge is defined as the work done in bringing one coulomb of charge from infinity to the point against the force created by the fixed charge,that is the potential is the work done per unit charge.
The electric field E, at the spherical surface is given by
(D). Boundary conditions on E and D,
As shown in fig.
It know that the electric field is conservative and hence the line integral of E.dL is zero around a closed path,
The tangential component of E is continuous across any boundary, that is Etan1 = E tan2
The normal component of D is continuous across any boundary except at the surface of conductor is generally
Dn1-Dn2= PS .
(C). Capacitor of isolated sphere of radius 1cm
C = 4πepsilon*rhi
R = 1cm = 0.01m
C = 4π epsilon * 0.01m
= 0.01/9*10^9
= 1.11*10^-12
C = 1.11 pf
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