Methods of Charging Objects - Friction, Conduction, and Induction

Conductor cant be charged by friction.
They are charged by
$(1)$ Induction
$(2)$ Conduction

The statement given is that "it is possible to charge objects without ever touching the objects to be charged". This statement is true. This charging process is called charging by induction. It is a process by which a charged body makes a conductor electrically charged without physical contact. The charges on a body by the process of induction are known as induced charges.

The rubber object becomes negatively charged since it would acquire electrons from fur. It would then charge then object A with negative charge since contact charging result in charging an object with same type of charge.

Due to friction, objects gets charged. The electrons are transferred between two objects. The material with greater electron affinity will receives electrons, and the other will lose electrons. Thus, object will A loses electrons and will acquires positive charge.

When we to touch an uncharged conductor with a charged conductor, the charged conductor shares the charge with uncharged conductor. This is called charging by conduction.

When the neutral metal sphere is touched with the negatively charged metal rod, both of them try to achieve same potential and hence some negative charge flows from rod to sphere for both of them to have negative charges.
Since the total charge is conserved, the sum of the negative charges in them would be equal to the originally present negative charge in the rod.

Free electrons in a material increases the mobility of flowing electrons into the material. The free electrons impact and transfer energy to each other. It increases the number of electrons that flow when same potential difference is applied.

If they are made to touch each other, the electrostatic conduction will occur. As a result the total charge will get distributed equally on both the balls because both the balls are identical in nature. 

By induction negative charge developes on surface of A close to B and positive charge developes on surface of A away from B, (when B carries positive charge). Therefore, overall potential of B decreases, charge of B remains unchanged.

Positively charged rod induces negative charge on the side of the sphere closer to the rod and an equal positive charge on the side away from the rod. When the rod is withdrawn, the negative charges move to neutralise the equal positive charge. The charge left is zero.

The metal cube is a conductor. The charge inside the conductor is zero. So the interior remains charge free. As it is isolated metal so when positive charge is brought near it , surface charge will become non-uniform.

When the two spheres are connected by a wire, the charge will flow between them till the potential between them will be same. Thus, the charge on each sphere is the average charge i.e $Q _{av}=\dfrac{-3+1}{2}=-1 C$

When a charged aluminum plate is touched to a neutral metal sphere then neutral metal sphere gets charged up. This happens due to which method of charging. This happens due to charging by conduction method.

When charging a conductor by induction, a charged object is brought close to but does not touch the conductor. In the end the conductor has charge of the opposite sign as the charge on the object.

Those with larger electron affinity will be more nagatively charged as it takes electrons from nylon.

True.

Given a conducting sphere, radius $4, cm$ has positive charge on it. This sphere is then connected to uncharged sphere of radius $1, cm$. So, when the two spheres are connected through a metal wire, the entire charge flow from charged to uncharged sphere i.e, electrons flow from $4, cm$ sphere to$1, cm$ sphere, leaving $4, cm$ radius sphere with net charge zero.

Using Gauss's law, the enclosed charge q(r) for a sphere with charge density rho = k * r^a is found by integrating the charge density over the volume. The electric field E(r) is proportional to q(r) / r^2. Setting up the ratio E(R/2) / E(R) = (1/8) and solving for a yields a = 2.

$R _B=2R _A$