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......$J$ $\left( {{\rm{Given}}\frac{{\rm{1}}}{{{\rm{4}}\pi {\varepsilon _{\rm{0}}}}} = 9 \times {{10}^9}\,\frac{{N{m^2}}}{{{C^2}}}} \right)$

A positively charged ring is in $y-z$ plane with its centre at origin. A positive test charge $q_0$, held at origin is released along $x$-axis, then its speed

There is $10$ units of charge at the centre of a circle of radius $10\,m$. The work done in moving $1\, unit$ of charge around the circle once is...........$units$

Which of the following statement$(s)$ is/are correct?

$(A)$ If the electric field due to a point charge varies as $r^{-25}$ instead of $r^{-2}$, then the Gauss law will still be valid.

$(B)$ The Gauss law can be used to calculate the field distribution around an electric dipole.

$(C)$ If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same.

$(D)$ The work done by the external force in moving a unit positive charge from point $A$ at potential $V_A$ to point $B$ at potential $V_B$ is $\left(V_B-V_A\right)$.

Two insulating plates are both uniformly charged in such a way that the potential difference between them is $V_2 - V_1 = 20\ V$. (i.e., plate $2$ is at a higher potential). The plates are separated by $d = 0.1\ m$ and can be treated as infinitely large. An electron is released from rest on the inner surface of plate $1. $ What is its speed when it hits plate $2?$
$(e = 1.6 \times 10^{-19}\ C, m_e= 9.11 \times 10^{-31}\ kg)$

Positive and negative point charges of equal magnitude are kept at $\left(0,0, \frac{a}{2}\right)$ and $\left(0,0, \frac{-a}{2}\right)$, respectively. The work done by the electric field when another positive point charge is moved from $(-a, 0,0)$ to $(0, a, 0)$ is