Four charges are placed on corners of a square as shown in figure having side of $5\,cm$. If $Q$ is one microcoulomb, then electric field intensity at centre will be

Two point charges $q_1\,(\sqrt {10}\,\,\mu C)$ and $q_2\,(-25\,\,\mu C)$ are placed on the $x-$ axis at $x = 1\,m$ and $x = 4\,m$ respectively. The electric field (in $V/m$ ) at a point $y = 3\,m$ on $y-$ axis is, [ take ${\mkern 1mu} {\mkern 1mu} \frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}{\mkern 1mu} {\mkern 1mu} N{m^2}{C^{ - 2}}{\rm{ }}$ ]

Three charges are placed as shown in figure. The magnitude of $q_1$ is $2.00\, \mu C$, but its sign and the value of the charge $q_2$ are not known. Charge $q_3$ is $+4.00\, \mu C$, and the net force on $q_3$ is entirely in the negative $x-$ direction. The magnitude of $q_2$ is

Two identical point charges are placed at a separation of $d$. $P$ is a point on the line joining the charges, at a distance $x$ from any one charge. The field at $P$ is $E$, $E$ is plotted against $x$ for values of $x$ from close to zero to slightly less than $d$. Which of the following represents the resulting curve

A charged oil drop is suspended in a uniform field of $3 \times$ $10^{4} V / m$ so that it neither falls nor rises. The charge on the drop will be $.....\times 10^{-18}\; C$

(take the mass of the charge $=9.9 \times 10^{-15} kg$ and $g=10 m / s ^{2}$ )

A thin conducting ring of radius $R$ is given a charge $+Q.$ The electric field at the centre $O$ of the ring due to the charge on the part $AKB$ of the ring is $E.$ The electric field at the centre due to the charge on the part $ACDB$ of the ring is