Electric Charge...

The electric field in a region is given by $$\vec { E } =a\hat { i } +b\hat { j } $$. Here a and b are constants. Find the net flux passing through a square area of side $${ L }_{ 0 }$$  parallel to y-z plane

Two small spheres each having the charge $$+Q$$ are suspended by insulated threads of length $$L$$ 

Twelve infinite long wire of uniform linear charge density $$\left( \lambda  \right)$$  are passing along the twelve edges of a cube. Find electric flux through any face of cube 

A conducting sphere of radius a has charge Q on it. It is enclosed by a neutral conducting concentric concentric spherical shell having inner radius 2a and outer radius 5a. Find electrostatic energy of system.

A non conducting sphere of radius $$'a'$$ has a type charge $$'+q'$$ uniformly distributed throughout in volume. A hollow spherical conductor having inner and  outer, radii $$'b'$$ and $$'c'$$ and net charge $$'-q'$$ is concentric with the sphere (see the figure)
Read the following statements
(i) The electric field at a distance $$r$$ from the center of the sphere $$ = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{qr}}{{{a^3}}}$$ for $$r<a$$.
(ii) The electric field at distance $$r$$ from the center of the sphere for $$a<r<b=0$$
(iii) The electric field at distance $$r$$ from the center of the sphere for $$ b<r<c<=0$$
(iv) The charge on the inner surface of the hollow sphere $$=-q$$
(v) The charge on the outer surface of the hollow sphere $$=+q$$.

A non conducting sphere of radius $$'a'$$ has a type charge $$'+q'$$ uniformly distributed throughout in volume. A hollow spherical conductor having inner and  outer, radii $$'b'$$ and $$'c'$$ and net charge $$'-q'$$ is concentric with the sphere (see the figure)
Read the following statements
(i) The electric field at a distance $$r$$ from the center of the sphere $$ = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{qr}}{{{a^3}}}$$ for $$r<a$$.
(ii) The electric field at distance $$r$$ from the center of the sphere for $$a<r<b=0$$
(iii) The electric field at distance $$r$$ from the center of the sphere for $$ b<r<c<=0$$
(iv) The charge on the inner surface of the hollow sphere $$=-q$$
(v) The charge on the outer surface of the hollow sphere $$=+q$$.

A charge of $$+2\mu C$$ is placed at $$x=0$$ and a charge of $$32\ \mu C$$ at $$x=60\ cm$$. A third charge $$Q$$ is placed on the $$x-$$axis, such that it experiences no force. The distance of the point from $$+2\mu C$$ is (in $$cm$$)

Two points charges $$Q$$ and $$-3Q$$ are placed at some distance apart. If the electric field at the location of $$Q$$ is $$E$$ then at the locality of $$-3Q$$, it is 

Two similar balls of mass 'm' are hung by a silk thread of length L and carry similar charge Q as shown in figure Assuming the separation to be small, the separation between the balls (denoted by x) is equal to

An inductor having $$400$$ turns, carrying of $$8 m A$$ and inductances $$5 mH$$ then flux is: