Question

A coaxial cable consists of a long cylindrical conductor of radius a=1 mm
concentric with a thin cylindrical shell of larger radius b=5 mm. If the central conductor has a charge per unit length ?=Q/L=1 micro(C)/m uniformly distributed on itssurface, what is the potential difference between the inner and outer conductors?

Answer 1

GivenRadius of inner cylinder a = 1 mm= ( 1 mm ) ( 10^-3 m / 1 mm )= 10^-3 mRadius of outer cylinder b = 5 mm=(5 mm ) ( 10^-3 m / 1 mm )= 5*10^-3 mCharge distributed on inner cylinderλ = Q / L= 1 μC / m= ( 1 μC / m ) ( 10^-6 C / 1 μC )= 10^-6 C / mElectric potential difference between coaxial cylinderV = ( Q / 2πε_o L )( ln ( b / a )= ( λ / 2πε_o ) ln ( b / a)=[ ( 10^-6 C / m ) / ( 2π*8.85*10^-12 C ² / N. m² ) ] ln ( 5 mm / 1 mm )=28943 V