Charge $q$ is uniformly distributed over a thin half ring of radius $R$. The electric field at the centre of the ring is

A positively charged thin metal ring of radius $R$ is fixed in the $xy - $ plane with its centre at the $O$. A negatively charged particle $P$ is released from rest at the point $(0,\,0,\,{z_0})$, where ${z_0} > 0$. Then the motion of $P$ is

Infinite charges of magnitude $q$ each are lying at $x =1,\, 2,\, 4,\, 8...$ meter on $X$-axis. The value of intensity of electric field at point $x = 0$ due to these charges will be

A ring of radius $R$ is charged uniformly with a charge $+\,Q$ . The electric field at a point on its axis at a distance $r$ from any point on the ring will be

The given diagram shows two semi infinite line of charges having equal (in magnitude) linear charge density but with opposite sign. The electric field at any point on $x$ axis for $(x > 0)$ is along the unit vector

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