Three identical charges are placed at the three corners of an equilateral triangle as shown in the figure. Which of the following statements is true for the electric field $E$ and electric potential $V$ at the center $O$?

Given below are two statements:
Statement-$I$: $A$ point charge is brought into an electric field. The value of the electric field at a point near the charge may increase if the charge is positive.
Statement-$II$: An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero.
Choose the correct answer from the options given below:

The adjacent diagram shows a charge $+Q$ held on an insulating support $S$ and enclosed by a hollow spherical conductor. $O$ represents the centre of the spherical conductor,and $P$ is a point such that $OP = x$ and $SP = r$. The electric field at point $P$ will be

Two equal negative charges are fixed at the points $(0, a)$ and $(0, -a)$ on the $y$-axis. $A$ positive charge $Q$ is released from rest at the point $(2a, 0)$ on the $x$-axis. The charge $Q$ will

Which of the following processes involves the principle of electrostatic induction?

Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(d, 0)$ respectively of a $(X, Y)$ coordinate system. Then: