Consider an electric field $$\overrightarrow E = {E_0}\widehat x$$ where $${E_0}$$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is

A uniformly charged thin spherical shell of radius $$R$$ carries uniform surface charge density of $$\sigma $$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $$F$$ (see figure). $$F$$ is proportional to

A tiny spherical oil drop carrying a net charge $$q$$ is balanced in still air with a vertical uniform electric field of strength $${{81\pi } \over 7} \times {10^5}\,\,V{m^{ - 1}}.$$ When the field is switched off, the drop is observed to fall with terminal velocity $$2 \times {10^{ - 3}}\,\,m{s^{ - 1}}.$$ Given $$g = 9.8\,m\,{s^{ - 2}},$$ viscosity of the air $$ = 1.8 \times {10^{ - 5}}\,\,Ns\,{m^{ - 2}}$$ and the density of coil $$=900$$ $$kg$$ $${m^{ - 3}},$$ the magnitude of $$q$$ is

A disk of radius $${a \over 4}$$ having a uniformly distributed charge 6C is placed in the xy-plane with its centre at ($$-$$a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4 to x = 5a/4. Two points charges $$-$$7C and 3C are placed at (a/4, $$-$$a/4, 0) and ($$-$$3a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces $$x=\pm a/2,y=\pm a/2,z=\pm a/2$$. The electric flux through this cubical surface is