An electric dipole is formed by two charges $+q$ and $-q$ located in $x y$-plane at $(0,2) \mathrm{mm}$ and $(0,-2) \mathrm{mm}$, respectively, as shown in the figure. The electric potential at point $P(100,100) \mathrm{mm}$ due to the dipole is $V_0$. The charges $+q$ and $-q$ are then moved to the points $(-1,2) \mathrm{mm}$ and $(1,-2) \mathrm{mm}$, respectively. What is the value of electric potential at $P$ due to the new dipole?

A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at its surface is V₀. A hole with a small area $$\alpha $$4$$\pi $$R²($$\alpha $$ << 1) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

The electric field $$E$$ is measured at a point $$P(0,0,d)$$ generated due to various charge distributions and the dependence of $$E$$ on $$d$$ is found to be different for different charge distributions. List-$${\rm I}$$ contains different relations between $$E$$ and $$d$$. List-$${\rm II}$$ describes different electric charge distributions, along with their locations. Match the functions in List-$${\rm I}$$ with the related charge distributions in List-$${\rm II}$$.

LIST - I		LIST - II
P.	$$E$$ is independent of $$d$$	1.	A point charge Q at the origin
Q.	$$E\, \propto \,1/d$$	2.	A small dipole with point charges $$Q$$ at $$\left( {0,0,l} \right)$$ and $$-Q$$ at $$\left( {0,0, - l} \right).$$ Take $$2l < < d$$
R.	$$E\, \propto \,1/{d^2}$$	3.	An infinite line charge coincident with the x-axis, with uniform linear charge density $$\lambda $$
S.	$$E\, \propto \,1/{d^3}$$	4.	Two infinite wires carrying uniform linear charge density parallel to the $$x$$-axis. The one along $$\left( {y = 0,z = l} \right)$$ has a charge density $$ + \lambda $$ and the one along $$\left( {y = 0,z = - l} \right)$$ has a charge density Take
		5.	Infinite plane charge coincident with the $$xy$$-plane with uniform surface charge density

Consider a uniform spherical charge distribution of radius $${R_1}$$ centred at the origin $$O.$$ In this distribution, a spherical cavity of radius $${R_2},$$ centred at $$P$$ with distance $$OP=a$$ $$ = {R_1} - {R_2}$$ (see figure) is made. If the electric field inside the cavity at position $$\overrightarrow r $$ is $$\overrightarrow E \overrightarrow {\left( r \right)} ,$$ then the correct statement(s) is (are)