Question

A circular plane sheet of radius $10\,cm$ is placed in a uniform electric field of $5 \times 10^5 \,N \,C^{-1}$, making an angle of $60^°$ with the field. The electric flux through the sheet is

• A. $1.36 \times 10^2\, N\, m^2\, C^{-1}$
• B. $1.36 \times 10^4\, N\, m^2\, C^{-1}$
• C. $0.515 \times 10^2\, N\, m^2\, C^{-1}$
• D. $0.515 \times 10^4\, N\, m^2\, C^{-1}$

Answer 1

Answer: (B)

Here, $r = 10 \,cm = 0.1\, m$, $E = 5 \times 10^5\, N\, C^{-1}$
As the angle between the plane sheet and the electric field is $60^°$, angle made by the normal to the plane sheet and the electric field is $\theta = 90^° - 60^° = 30^°$
$\phi_{E}=ES\,cos\theta=E\times\pi r^{2}\,cos\theta$
$=5\times10^{5}\times3.14\times\left(0.1\right)^{2}cos30^{°}=1.36\times10^{4}\,N\,m^{2}\,C^{-1}$