A charge <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math> is surrounded by a closed surface consisting of an inverted cone of height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> and base radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math>, and a hemisphere of radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> as shown in the figure. The electric flux through the conical surface is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>n</mi><mn>6</mn></mfrac><mfrac><mi>q</mi><msub><mi>ε</mi><mn>0</mn></msub></mfrac></math> (in SI units). The value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> is _______. [2022] <img alt="" src="https://smartachievers.online/public/adv26/672.jpg" />

(3) ϕ cone = q 2 ε 0 = 3 q 6 ε 0 ∴ n = 3

A charge is surrounded by a closed surface consisting of an inverted cone of height and base radius , and a hemisphere of radius as shown in the figure. The electric flux through the conical surface is (in SI units). The value of is ______

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Solution

Q.
A charge $q$ is surrounded by a closed surface consisting of an inverted cone of height $h$ and base radius $R$ , and a hemisphere of radius $R$ as shown in the figure. The electric flux through the conical surface is $\frac{n}{6} \frac{q}{ε_{0}}$ (in SI units). The value of $n$ is _______. [2022]

Solution

Ans.
(3)

$ϕ_{cone} = \frac{q}{2 ε_{0}} = \frac{3 q}{6 ε_{0}}$

$∴$ $n = 3$

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Solution

Q. A charge q is surrounded by a closed surface consisting of an inverted cone of height h and base radius R, and a hemisphere of radius R as shown in the figure. The electric flux through the conical surface is n6qε0 (in SI units). The value of n is _______. [2022]

Ans. (3) ϕcone=q2ε0=3q6ε0 ∴ n=3

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Ans.
(3)

$ϕ_{cone} = \frac{q}{2 ε_{0}} = \frac{3 q}{6 ε_{0}}$

$∴$ $n = 3$