A point charge q = 8.85 × 1 0 − 9 C is placed at (0, d, 0) where d = 1 m . An insulating surface ABCA is on the x-z plane, which is bounded by a quarter circle AB and two equal length straight lines B

Question

A point charge q = 8.85 × 1 0 − 9 C is placed at (0, d, 0) where d = 1 m . An insulating surface ABCA is on the x-z plane, which is bounded by a quarter circle AB and two equal length straight lines BC and CA as shown in the figure. Electric flux through the surface ABCA (in N m 2 /C ) is :- (nearest integer) (Take ε 0 ​ = 8.85 × 1 0 − 12 N m 2 C 2 ​ )

TestHub · Accepted Answer

Solid-angle method. Flux through the full d x d square below q (q above its corner): $ϕ_{1} = \frac{q}{24 ε _{0}}$ .

Flux through the quarter disc of radius d: $ϕ_{2} = \frac{q}{8 ε _{0}} (1 - \frac{1}{2})$ .

ABCA = square minus quarter disc: $ϕ = \frac{q}{24 ε _{0}} - \frac{q}{8 ε _{0}} + \frac{q}{8 2 ε _{0}} = \frac{q}{ε _{0}} (0.00505)$ .

$\frac{q}{ε _{0}} = \frac{8.85 \times 1 0 ^{- 9}}{8.85 \times 1 0 ^{- 12}} = 1000 \Rightarrow ϕ = 5.05 \approx 5 N m^{2} /C$ . Answer: 5.

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