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

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 made by plane surfaces Ω = 2 × 2 π ( 1 − cos θ ) ⇒ Ω = 4 π − 4 π cos θ So solid angle made by curved surface = 4 π − Ω = 4 π − ( 4 π − 4 π cos θ ) = 4 π cos θ ϕ 3 0 ∘ ​ = ϕ = 4 π 4 π c o s 3 0 ∘ ​ ε 0 ​ Q ​ = cos 3 0 ∘ ε 0 ​ Q ​ ϕ 60 ​ = 4 π 4 π c o s 6 0 ∘ ​ ε 0 ​ Q ​ = cos 6 0 ∘ ε 0 ​ Q ​ ϕ 60 ​ ϕ 30 ​ ​ = c o s 6 0 ∘ c o s 3 0 ∘ ​ = 3 ​ ϕ 60 ​ ϕ ​ = 3 ​ ⇒ ϕ 60 ​ = 3 ​ ϕ ​ ⇒ n = 3

Physics - Electrostatics Question with Solution | TestHub

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