Q. One-fourth of a sphere of radius R is removed as shown in figure. An electric field E exists parallel to the *xy* . Find the flux through the remaining curved part.

(a) πR²E

(b) √2 πR²E

(c) πR²E /√2

(d) none of these

Ans: (c)

Sol:

$ \displaystyle \vec{S_1} = \frac{\pi R^2}{2}(-\hat{i})$

$ \displaystyle \vec{S_2} = \frac{\pi R^2}{2}(-\hat{j})$

$ \displaystyle \vec{E} = Ecos45 \hat{i} + Esin45 \hat{j}$

Flux $\displaystyle \phi = \vec{E}.\vec{S}$