The charge per unit length of the four quadrant of the ring is $2\ \lambda , - 2\ \lambda , \lambda$ and $- \lambda$ respectively. The electric field at the centre is
$-$ $\frac{\lambda }{{2\pi {\varepsilon _0}R}}\,\hat i$
$\frac{\lambda }{{2\pi {\varepsilon _0}R}}\,\hat j$
$\frac{{\sqrt 2 \,\,\lambda }}{{4\pi {\varepsilon _0}R}}\,\hat i$
None
Select the correct statement : (Only force on a particle is due to electric field)
A charge $Q$ is distributed over a line of length $L.$ Another point charge $q$ is placed at a distance $r$ from the centre of the line distribution. Then the force expericed by $q$ is
Two point charges $q_{ A }=3\; \mu \,C$ and $q_{ B }=-3\; \mu \,C$ are located $20\; cm$ apart in vacuum.
$(a)$ What is the electric field at the midpoint $O$ of the line $AB$ joining the two charges?
$(b)$ If a negative test charge of magnitude $1.5 \times 10^{-9}\; C$ is placed at this point, what is the force experienced by the test charge?
Two point charges $q_{1}$ and $q_{2},$ of magnitude $+10^{-8} \;C$ and $-10^{-8}\; C ,$ respectively, are placed $0.1 \;m$ apart. Calculate the electric fields at points $A, B$ and $C$ shown in Figure
Suppose a uniformly charged wall provides a uniform electric field of $2 \times 10^4 \mathrm{~N} / \mathrm{C}$ normally. A charged particle of mass $2 \mathrm{~g}$ being suspended through a silk thread of length $20 \mathrm{~cm}$ and remain stayed at a distance of $10 \mathrm{~cm}$ from the wall. Then the charge on the particle will be $\frac{1}{\sqrt{\mathrm{x}}} \ \mu \mathrm{C}$ where $\mathrm{x}=$ ____________. use $g=10 \mathrm{~m} / \mathrm{s}^2$ ]