A conic surface is placed in a uniform electric field E as shown such that field is perpendicular to the surface on the side A B. The base of the cone is of radius R and height of the cone is h. The angle of cone is θ as shown. Find the magnitude of that flux which enters the cone curved surface from left side. Don't count the outgoing flux. (θ

Question

A conic surface is placed in a uniform electric field E as shown such that field is perpendicular to the surface on the side A B. The base of the cone is of radius R and height of the cone is h. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/9c6ef676e3e3daf85743899bd0664635-.png" /> The angle of cone is θ as shown. Find the magnitude of that flux which enters the cone curved surface from left side. Don't count the outgoing flux. (θ<45°) (A) E R[h cos θ+π(R / 2) sin θ] (B) E R[h sin θ+π(R / 2) cos θ] (C) E R[h cos θ+π R sin θ] (D) None of these

Tardigrade Admin · Accepted Answer

Flux entering the cone from side A B will ultimately also pass through area A1 and A2. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/cf31c6a36dfa70ec850e50b6d4fd82cb-.png" /> So, φ=E A1 cos θ+E A2 cos (90°-θ) =E((1/2) 2 R h cos θ+(π/2) R2 sin θ) =E R(h cos θ+π(R / 2) sin θ)

$ER [h cos θ + π (R /2) sin θ]$

$ER [h sin θ + π (R /2) cos θ]$

$ER [h cos θ + π R sin θ]$

None of these

Flux entering the cone from side $A B$ will ultimately also pass through area $A_{1}$ and $A_{2}$ .

So, $ϕ = E A_{1} cos θ + E A_{2} cos (9 0^{\circ} - θ)$
$= E (\frac{1}{2} 2 R h cos θ + \frac{π}{2} R^{2} sin θ)$
$= ER (h cos θ + π (R /2) sin θ)$

ER[hcosθ+π(R/2)sinθ]

ER[hsinθ+π(R/2)cosθ]

ER[hcosθ+πRsinθ]

None of these

Flux entering the cone from side AB will ultimately also pass through area A1​ and A2​. So, ϕ=EA1​cosθ+EA2​cos(90∘−θ) =E(21​2Rhcosθ+2π​R2sinθ) =ER(hcosθ+π(R/2)sinθ)

$ER [h cos θ + π (R /2) sin θ]$

$ER [h sin θ + π (R /2) cos θ]$

$ER [h cos θ + π R sin θ]$

Flux entering the cone from side $A B$ will ultimately also pass through area $A_{1}$ and $A_{2}$ .

So, $ϕ = E A_{1} cos θ + E A_{2} cos (9 0^{\circ} - θ)$
$= E (\frac{1}{2} 2 R h cos θ + \frac{π}{2} R^{2} sin θ)$
$= ER (h cos θ + π (R /2) sin θ)$