A cylinder is uniformly charged on its curved surface with charge density σ = π 1 × 1 0 − 9 C / m 2 . Radius of the cylinder is R = 10 cm . Calculate the electric field (in V / m ) at the axis of cy

Question

A cylinder is uniformly charged on its curved surface with charge density σ = π 1 ​ × 1 0 − 9 C / m 2 . Radius of the cylinder is R = 10 cm . Calculate the electric field (in V / m ) at the axis of cylinder, as shown in the figure. Given : θ 2 ​ = 5 3 ∘ & θ 1 ​ = 3 7 ∘

TestHub · Accepted Answer

​ d q = σ ( 2 π R ) ( d x ) ​ d E = ( R 2 + x 2 ) 3/2 K ( d q ) ( x ) ​ = K σ ( 2 π R ) ​ R = x tan θ ​ 0 = ( d x ) tan θ + x ⋅ sec 2 θ d θ ​ d E = − x 3 ( sec 3 θ ) tan θ K σ ( 2 π R ) ( x ) ( x sec 2 θ ) d θ ​ ​ = − K σ ( 2 π ) ∫ + θ 2 ​ + θ 1 ​ ​ cos θ d θ ​ = − K σ ( 2 π ) sin θ ∫ + θ 2 ​ + θ 1 ​ ​ ​ = − K σ ( 2 π ) ( sin θ 1 ​ + sin θ 2 ​ ) ​ = 9 × 1 0 9 × π 1 ​ × 1 0 − 9 × 2 π ( 5 3 ​ − 5 4 ​ ) ​ = 3.6 ​

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