A solid conducting sphere of radius a has a net positive charge 2Q. A conducting spherical shell of inner radius b and outer radius c is concentric with the solid sphere and has a net charge –Q. The surface charge density on the inner and outer surfaces of the spherical shell will be?

(1) $-\frac{2\mathrm{Q}}{4{\mathrm{\pi b}}^2},<mspace\; width="1em"></mspace>\frac{\mathrm{Q}}{4{\mathrm{\pi c}}^2}$

(2) $-\frac{\mathrm{Q}}{4{\mathrm{\pi b}}^2},<mspace\; width="1em"></mspace>\frac{\mathrm{Q}}{4{\mathrm{\pi c}}^2}$

(3) $0,<mspace\; width="1em"></mspace>\frac{\mathrm{Q}}{4{\mathrm{\pi c}}^2}$

(4) None of the above

A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by 

(1) $2\pi R^{2}E$

(2) $\pi R^2/E$

(3) $(\pi R^2-\pi R)/E$ 

(4) Zero

Total electric flux coming out of a unit positive charge put in air is:
1. \(\varepsilon _0\)
2. \(\varepsilon _0^{-1}\)
3. \((4\pi\varepsilon _0)^{-1}\)
4. ​​​​​\(4 \pi\varepsilon _0\)

A cube of side l is placed in a uniform field E, where $E=E\hat{i}$. The net electric flux through the cube is

(1) Zero

(2) l²E

(3) 4l²E

(4) 6l²E

Electric charge is uniformly distributed along a long straight wire of radius \(1\) mm. The charge per cm length of the wire is \(Q\) coulomb. Another cylindrical surface of radius \(50\) cm and length \(1\) m symmetrically encloses the wire as shown in the figure. The total electric flux passing through the cylindrical surface is: