A ring of charge with radius $0.5\, m$ having a $0.02\, m$ gap, carries a charge of $+1\, C$. The field at the centre is

Select the correct statement : (Only force on a particle is due to electric field)

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

The electric field due to a charge at a distance of $3\, m$ from it is $500\, N/coulomb$. The magnitude of the charge is.......$\mu C$ $\left[ {\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {{10}^9}\,\frac{{N - {m^2}}}{{coulom{b^2}}}} \right]$

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?

A cube of side $'a'$ has point charges $+Q$ located at each of its vertices except at the origin where the charge is $- Q$. The electric field at the centre of cube is