Four identical charges $ + \,50\,\mu C$ each are placed, one at each corner of a square of side $2\,m$. How much external energy is required to bring another charge of $ + \,50\,\mu C$ from infinity to the centre of the square......$J$ $\left( {{\rm{Given}}\frac{{\rm{1}}}{{{\rm{4}}\pi {\varepsilon _{\rm{0}}}}} = 9 \times {{10}^9}\,\frac{{N{m^2}}}{{{C^2}}}} \right)$

$n$ the rectangle, shown below, the two corners have charges ${q_1} = - 5\,\mu C$ and ${q_2} = + 2.0\,\mu C$. The work done in moving a charge $ + 3.0\,\mu C$ from $B$ to $A$ is.........$J$ $(1/4\pi {\varepsilon _0} = {10^{10}}\,N{\rm{ - }}{m^2}/{C^2})$

Two points $P$ and $Q$ are maintained at the potentials of $10\, V$ and $-4\,V$, respectively. The work done in moving $100$ electrons from $P$ and $Q$ is

Figures $(a)$ and $(b)$ show the field lines of a positive and negative point charge respectively

$(a)$ Give the signs of the potential difference $V_{ P }-V_{ Q } ; V_{ B }-V_{ A }$

$(b)$ Give the sign of the potential energy difference of a small negative charge between the points $Q$ and $P ; A$ and $B$.

$(c)$ Give the sign of the work done by the field in moving a small positive charge from $Q$ to $P$.

$(d)$ Give the sign of the work done by the external agency in moving a small negative charge from $B$ to $A$.

$(e)$ Does the kinetic energy of a small negative charge increase or decrease in going from $B$ to $A?$

If $4 \times {10^{20}}eV$ energy is required to move a charge of $0.25$ coulomb between two points. Then what will be the potential difference between them......$V$

If $OP = 1\,\,cm$ and $OS = 2\,\, cm$, work done by electric field in shifting a point charge $\frac {4\sqrt 2}{27}\,\, μC$ from point $P$ to $S$ in given figure is