Two concentric cylinder have a radius a and b. The charge on the cylinder is +q and -q. Another cylinder of radius (a+b)/2 is introduced between the two. The charge on this cylinder is +q/2. What is the capacitance of the arrangement??
(consider the inner and the outer most point).
62what about the spheres...
There is a set of spheres.. and there is a set of cylinder.. and there is another cylinder
but what is the relation between them!!
62NOw it depends on which two cylinders are the ones you connect to the circuit?
the original ones? (Which is most likely)
Then find the electric field at the center.. then find the work done in moving from one surface of the cylinder to the other cylinder
Can you try that?
1
Connecting the original ones to the circuit, we have to find
Va-Vc= (Va-Vb)+(VB-Vc)
Find electric field using gauss law. Two cases follow-
a<r<a+b/2
and
a+b/2<r<b
φ=E(2πrl)=q/ξ0
Va-Vb=∫E.dr
limits→a to a+b/2
Solving we get Va-Vb= q(ln a+b/2)/2πε0l
Similarly we get Vb-Vc
C=q/ΔV
=(2πε0l)/[1.5 ln(2b)-ln(2a)-0.5ln(a+b)]
