Electric Charge...

An electron with a speed of $$4×10^6$$ m/s enters an electric field of magnitude $$10^5$$N/C traveling along field lines in the direction that retards its motion. Calculate the minimum length of the electric field region in the direction of motion required to stop the electron momentarily within the field region.

A ball of charge to mass ratio $$8 \mu C/g$$ is placed at a distance of $$10 cm$$ from the wall. An electric field $$100\ N/m$$ is switched on in the direction of wall. Find the time period of its oscillations. Assume all collisions elastic.

A charge $$Q$$ is divided into $$q$$ and $$(Q - q)$$. If $$\dfrac {Q}{q} = x$$, such that the repulsion between them is maximum, find $$x$$.

A hemispherical body is placed in a uniform electric field E. What is the flux linked with curved surface, if field is perpendicular to base in figure.

Consider a uniform electric field $$E=3\times 10^3 \hat i \: N/C$$. What is the flux of this field through a square of $$10\  cm$$ on a side whose plane is parallel to the yz plane?

In the figure shown, A is a fixed charged. B (of mass m) is given a velocity $$v$$ as shown in figure. At this moment the radius of curvature of the resultant path of B is :

A particle of charge $$-q$$ and mass $$m$$ moves in a circular orbit of radius $$r$$ about a fixed charge $$+Q$$. The relation between the radius of the orbit $$r$$ and the time period $$T$$ is:

Two point charges placed at a distance $$r$$ in air exert a force $$F$$ on each other. The value of distance $$R$$ at which they experience force $$4F$$ when placed in a medium of dielectric constant $$K = 9$$ is :

A positive point charge $$+Q$$ is fixed in space. A negative point charge $$q$$ of mass $$m$$ revolves around the fixed charge in an elliptical orbit. The fixed charge $$+Q$$ is at one focus of the ellipse. The only force acting on the negative charge is the electrostatic force due to the positive charge. Then which of the following statements is true?

Electric flux through a surface of area $$100\ m^{2}$$ lying in the xy plane is (in V-m) if $$\vec{E}=\hat{i}+\sqrt{2}\hat{j}+\sqrt{3\hat{k}}$$