Coaxial cylinders: A long metal cylinder with a radius a is supported on an insulating stand on the axis of a long, hollow, metal tube with radius b.

Elleanor Mckenzie

Elleanor Mckenzie

Answered question

2021-01-28

Coaxial cylinders:
On the axis of a lengthy hollow metal tube with a radius of b, a long metal cylinder with a radius of an is supported on an insulating stand. On the inner cylinder, the positive charge per unit length is? , and there is an equal negative charge per unit length on the outer cylinder. (a) calculate the potential V(r) for:
i) r<a
ii) a<r<b
iii) r>b
Take V=0 at r=b

Answer & Explanation

l1koV

l1koV

Skilled2021-01-29Added 100 answers

a) (i) V=λ2πϵ0(ln(ba)ln(bb))=λ2πϵ0ln(ba)
(ii) V=λ2πϵ0(ln(br)ln(bb))=λ2πϵ0ln(br)
(iii) V=0
b) Vab=V(a)V(b)=λ2πϵ0ln(ba)
c) Between the cylinders:
V=λ2πϵ0ln(br)=Vabln(ba)ln(br)
E=dVdr=Vabln(ba)ddr(ln(br))=Vabln(ba)1r
d) The potential difference between the two cylinders is identical to that in part (b) even if the outer cylinder has no charge.

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