A charge is kept at the central point P of a cylindrical region. The two edges subtend a half-angle θ at P, as shown in the figure. When θ = 3 0 ∘ , then the electric flux through the curved surface o

Question

A charge is kept at the central point P of a cylindrical region. The two edges subtend a half-angle θ at P, as shown in the figure. When θ = 3 0 ∘ , then the electric flux through the curved surface of the cylinder is Φ . If θ = 6 0 ∘ , then the electric flux through the curved surface becomes Φ/ n ​ , where the value of n is ____ .

TestHub · Accepted Answer

Solid angle of the two end faces at P: Ω = 2 × 2 π ( 1 − cos θ ) = 4 π ( 1 − cos θ ) . Flux through the curved surface = ( q / ε 0 ​ ) ( 4 π − Ω ) /4 π = ( q / ε 0 ​ ) cos θ . Φ 30 ​ / Φ 60 ​ = cos 3 0 ∘ / cos 6 0 ∘ = 3 ​ ⇒ Φ 60 ​ = Φ/ 3 ​ , hence n = 3 .

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