Question

A long insulating rod suspended by insulating wires.Assume that the rod is initially electrically neutral. Forconvenience, we will refer to the left end of the rod as end A, andthe right end of the rod as end B . In the answer options for thisproblem, "weakly attracted/repelled" means "attracted/repelled witha force of magnitude similar to that which would exist between twoballs, one of which is charged, and the other acquires a smallinduced charge". An attractive/repulsive force greater than thisshould be classified as "strongly attracted/repelled".

Part A

A small metal ball is given a negativecharge, then brought near (i.e., within a few millimeters) to end Aof the rod. What happens to end A of the rod when the ballapproaches it closely this first time?

It is strongly repelled. It is stronglyattracted. It is weakly attracted. It is weakly repelled.Or it is neither attracted nor repelled.

Now consider what happens when thesmall metal ball is repeatedly given a negative charge andthen brought into contact with end A of the rod

Part B

After several contacts with the chargedball, how is the charge on the rod arranged?

positive charge on end B and negativecharge on end A.
negative charge spread evenly on both ends
negative charge on end A with end B remaining almost neutral
positive charge on end A with end B remaining almost neutral
none of the above

Part C

How does end A of the rod react when the ballapproaches it after it has already made several contacts with therod, such that a fairly large charge has been deposited at endA?

It is strongly repelled. It is stronglyattracted. It is weakly attracted. It is weakly repelled. It isneither attracted nor repelled.

Answer 1

Concepts and reason

The concepts required to solve this problem are the electrostatic force and the charging by induction.

Initially, using the concept of the charging by induction, find the charge on the rod due to the negatively charged metallic ball. Then, determine the nature of the electrostatic force present between the ball and the rod depending on the type of charges present between them.

Later, using the concept of the charging by conduction, find the charge on the rod due to the negatively charged metallic ball. Then, determine the nature of the electrostatic force present between the ball and the rod depending on the type of charges present between them.

Finally, depending on the type of charge present in the ball and the charge present at the end of the end point A of the rod, determine the nature of the electrostatic force between them.

Fundamentals

The electrostatic induction is a redistribution of electric charges on an object due to influence of nearby charges. According to the sign of charge on the charged body, positive charge develops one end and negative on the other side.

When an uncharged object is brought in contact with a charged object, the uncharged object gets charged by the transfer of electrons from the charged object and this process of the charging is known as charging by conduction.

(A)

When the negatively charged ball is moved close to the end $A$, a positive charge induces at the end $A$ of the rod and equal negative charge at the other end. Hence, the ball is attracted towards end $A$ because the ball is negatively charged and the end point is positively charged.

As the charge flow is impressed by the insulator, so the induced charge is small and the attraction is weak.

(B)

After the several contacts of the end point A of the rod with the negative charged ball, negative charge deposits at the end $A$ of the rod.

But the charge flow is repressed in an insulator. Hence, the negative charge will more or less stay there and doesn’t spread out over the entire rod.

Hence, the end $A$ of the rod is negatively charged and end $B$ of the rod remains neutral.

(C)

The negatively charged ball has made several contacts with the end point A of the rod. Therefore, due to the charging by conduction, the end point A of the rod has more amount of negative charge.

When the negatively charged ball approaches the negatively charged end point A of the rod, the ball will be repelled strongly due the fact that the like charges show the repelling nature of electrostatic force.

Thus, due to the presence of more amount of negative charge on the end point of the rod, the ball will be repelled strongly, not weakly.

The electrostatic force between the end point of the rod and the ball cannot be attractive because the types are of same nature and the like charges show the repelling behavior of the electrostatic force.

Ans: Part A

The end $A$ of the rod is weakly attracted, when the ball approaches it closely first time.