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
$1.02 \times {10^7}N/C$ upwards
$2.04 \times {10^7}N/C$ downwards
$2.04 \times {10^7}N/C$ upwards
$1.02 \times {10^7}N/C$ downwards
A uniformly charged rod of length $4\,m$ and linear charge density $\lambda = 30\,\mu C/m$ is placed as shown in figure. Calculate the $x-$ component of electric field at point $P$.
Equal charges $q$ are placed at the vertices $A$ and $B$ of an equilateral triangle $ABC$ of side $a$. The magnitude of electric field at the point $C$ is
A point charge of $10\,\mu C$ is placed at the origin. At what location on the $X$-axis should a point charge of $40\,\mu\,C$ be placed so that the net electric field is zero at $x =2\,cm$ on the $X$-axis ?
Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is $\alpha$. The spheres are now immersed in a dielectric liquid of density $800 kg m ^{-3}$ and dielectric constant $21$ . If the angle between the strings remains the same after the immersion, then
$(A)$ electric force between the spheres remains unchanged
$(B)$ electric force between the spheres reduces
$(C)$ mass density of the spheres is $840 kg m ^{-3}$
$(D)$ the tension in the strings holding the spheres remains unchanged
In the given figure distance of the point from $A$ where the electric field is zero is......$cm$