Two electrons each are fixed at a distance $'2d'$. A third charge proton placed at the midpoint is displaced slightly by a distance $x ( x << d )$ perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : $( m =$ mass of charged particle)
$\left(\frac{2 q^{2}}{\pi \varepsilon_{0} m d^{3}}\right)^{\frac{1}{2}}$
$\left(\frac{\pi \varepsilon_{0} md ^{3}}{2 q ^{2}}\right)^{\frac{1}{2}}$
$\left(\frac{ q ^{2}}{2 \pi \varepsilon_{0} md ^{3}}\right)^{\frac{1}{2}}$
$\left(\frac{2 \pi \varepsilon_{0} md ^{3}}{ q ^{2}}\right)^{\frac{1}{2}}$
Three equal charges $+q$ are placed at the three vertices of an equilateral triangle centred at the origin. They are held in equilibrium by a restoring force of magnitude $F(r)=k r$ directed towards the origin, where $k$ is a constant. What is the distance of the three charges from the origin?
Two charged spheres separated at a distance $d$ exert a force $F$ on each other. If they are immersed in a liquid of dielectric constant $2$, then what is the force (if all conditions are same)
Consider two point charges of equal magnitude and opposite sign separated by a certain distance. The neutral point due to them
Two identical metallic spheres $A$ and $B$ when placed at certain distance in air repel each other with a force of $F$. Another identical uncharged sphere $C$ is first placed in contact with $A$ and then in contact with $B$ and finally placed at midpoint between spheres $A$ and $B$. The force experienced by sphere $C$ will be.
The ratio of gravitational force and electrostatic repulsive force between two electrons is approximately (gravitational constant $=6.7 \times 10^{-11} \,Nm ^2 / kg ^2$, mass of an electron $=9.1 \times 10^{-31} \,kg$, charge on an electron $=1.6 \times 10^{-19} C$ )