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

Which of the field patterns given below is valid for electric field as well as for magnetic field ?

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 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