Question 2 only 1. Stepwise Derivation of the Capacitance of a Linear Filament a

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Question 2 only

1. Stepwise Derivation of the Capacitance of a Linear Filament and of a Concentric Cylindrical Sheath (a) Determine the electric field at all points in sold metal filament of radius, A, carrying a total charge, +Q, within a larger, hollow cylindrical metal sheath of radius, B, carrying a total charge, -Q. You should assume that the cylindrical sheath is concentric to the metal filament. (b) Determine the electric potential difference between the surfaces of the two conductors. (c) Determine the capacitance of the pair of conductive bodies. (d) Examine the appropriate limiting case of your space (you will need to divide space into appropriate regions) for a answer to the previous part to express and comment on the capacitance (not the capacitance per length) of the system as (BA)

Explanation / Answer

2] we know that, Q = CV or C = Q/V. Let charge on each surface be Q and -Q, so we can say that charge of capacitor is Q.

potential at outer surface = kQ/rB - kQ/rA = 0.

potential at inner surface = kQ/rA - kQ/rB

C = Q/V = 1/[k/rA - k/rB] = 4pi e0 rA*rB / [ rB- rA]

C = 4pi e0 rA*rB / [rB- rA]

hence derived.

b] capacitance of single charged sphere, C=0 because rA will be zero in that case

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