Six charges $+ q ,- q ,+ q ,- q ,+ q$ and $- q$ are fixed at the corners of a hexagon of side $d$ as shown in the figure. The work done in bringing a charge $q _0$ to the centre of the hexagon from infinity is :$\left(\varepsilon_0-\right.$ permittivity of free space)
$0$
$\frac{- q ^2}{4 \pi \varepsilon_0 d }$
$\frac{- q ^2}{4 \pi \varepsilon_0 d }\left(3-\frac{1}{\sqrt{2}}\right)$
$\frac{-q^2}{4 \pi \varepsilon_0 d }\left(6-\frac{1}{\sqrt{2}}\right)$
Two point charges $100\,\mu \,C$ and $5\,\mu \,C$ are placed at points $A$ and $B$ respectively with $AB = 40\,cm$. The work done by external force in displacing the charge $5\,\mu \,C$ from $B$ to $C$, where $BC = 30\,cm$, angle $ABC = \frac{\pi }{2}$ and $\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}\,N{m^2}/{C^2}$.........$J$
An electron enters in high potential region ${V_2}$ from lower potential region ${V_1}$ then its velocity
For an infinite line of charge having charge density $\lambda $ lying along $x-$ axis, the work required in moving charge $q$ from $C$ to $A$ along arc $CA$ is :-
A charge of $10\, e.s.u.$ is placed at a distance of $2\, cm$ from a charge of $40\, e.s.u.$ and $4\, cm$ from another charge of $20\, e.s.u.$ The potential energy of the charge $10\, e.s.u.$ is (in $ergs$)
A proton is accelerated through $50,000\, V$. Its energy will increase by