Question

A hemispherical body is placed in a uniform electric field E. What is the flux linked with the curved surface if the field is perpendicular to the curved surface at every points as in figure.

• A. $\varphi =E4\pi R^2$
• B. $\varphi =E2\pi R^2$
• C. $\varphi =E7\pi R^2$
• D. $\varphi =E9\pi R^2$

Answer 1

The correct option is B $\varphi =E2\pi R^2$

For (c)
The field is not uniform it is radial, so normal to the curved surface and electric field are in same direction. So, flux linked with curved surface will be given by:
${\varphi }_{CS}=E\frac{1}{2}\left(4\pi R^2\right)cos0=2\pi R^{2}E$