Electric Charge...

Two charges, each equal q, are kept at $$x=-a$$ and $$x=a$$ on the x-axis. A particle of mass $$m$$ and charge $${q_0} = \frac{q}{2}$$ is placed at the origin. If  charge $${q_0}$$ is given a small displacement $$(y<<a)$$ along the y-axis, the net force acting on the particle is proportional to: 

Two insulated, similar copper spheres $$A$$ and $$B$$ are separated by a distance of $$0.5$$ m. Each sphere carries a charge of $$6.5 \times {10^{ - 7}}C$$.

Two small identical spheres each of mass $$1\ g$$ and carrying same charge $${10}^{-9}$$ care suspended by threads of equal lengths. If the distance between the centres of the spheres is $$0.3\ cm$$ in equilibrium then the inclination of the thread with the vertical will be:-

A point charge $$q=10^{-11}\ C$$, is placed at $$4\ cm$$ above a square plate $$(8\ cm\ \times 8\ cm)$$, having charge density $$0.5\ \times 10^{-8}\ C/m^{2}$$. Find the flux related with it.

The volume charge density as a function of distance $$x$$ from one face inside a unit cube is varying as shown in the figure. Then the total flux $$(in S.I units)$$ through the cube if $$(p-{0}=8085\times10^{-12}Cm^{3})$$ is

The electric field in a region of space is given by $$E=(5\ \hat {i}+2\hat {j})N/C$$. The electric flux through an area of $$2\ m^{2}$$ lying in the $$YZ$$ plane, in $$S.I.$$. units is ?

A charge q is distributed uniformly on a ring of radius R. A sphere of equal radius R is constructed with its centre at the periphery of the ring, Find the flux of the electric field through the surface of the sphere

The small spherical balls each carrying a charge $$Q = 10 \mu$$  $$C$$ are suspended by two insulting threads of equal length $$1m$$ each, from a point fixed in the  cielling. It is found that is in equilibrium threads are separated by an angle $${60^ \circ}$$ between them, as shown in the figure. What is the tension in the threads (Given : $$\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}Nm/{C^2}$$)

What is the electric flux linked with closed surface?

Two point charges placed at a distance 'r' in air exert a force F. The value of distance at which they exerts same force when placed in medium (dielectric constant K) is :-