Two equal positive point charges are separated by a distance $2 a$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $q_0$ becomes maximum is $\frac{a}{\sqrt{x}}$. The value of $x$ is $................$

A cube of side $b$ has a charge $q$ at each of its vertices. The electric field due to this charge distribution at the centre of this cube will be

Two charges placed in air repel each other by a force of ${10^{ - 4}}\,N$. When oil is introduced between the charges, the force becomes $2.5 \times {10^{ - 5}}\,N$. The dielectric constant of oil is

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Two identical balls having like charges and placed at a certain distance apart repel each other with a certain force. They are brought in contact and then moved apart to a distance equal to half their initial separation. The force of repulsion between them increases $4.5$ times in comparison with the initial value. The ratio of the initial charges of the balls is

A conducting sphere of radius $R$, and carrying a charge $q$ is joined to a conducting sphere of radius $2R$, and carrying a charge $-2q$. The charge flowing between them will be