Question

Figure 21-12 shows three pairs of identical spheres that are to be touched together and then separated. The initial charges on them are indicated. Rank the pairs according to (a) the magnitude of the charge transferred during touching and (b) the charge left on the positively charged sphere, greatest first.

Short answer

1. The rank of the pairs according to the magnitude of the charge transferred during touching is $\left|Q_3\right|\ge \left|Q_1\right|\ge \left|Q_2\right|.$
2. The rank of the pairs according to the charge left on the positively charged sphere is$q_1=q_2=q_3.$

Step-by-step solution

Stating the given data

Figure 21-12 represents three pairs of identical spheres with their charges indicated on them.

Understanding the concept of charging by conduction

When two charged bodies are brought in contact with each other, the total charge of the system is divided among the given charged bodies equally until both have the same charge as per their volume. This process is called charging by conduction. Thus, using this concept, the charges on each body can be calculated.

a) Calculation of the rank according to the magnitude of the charge transferred during touching

As per the concept, the charge acquired by bodies during touching in pair (1) is given as

$$\begin{gathered} q_1=\frac{+6e-4e}{2} \\ =\frac{+2e}{2} \\ =+e \end{gathered}$$

Now, the magnitude of the amount of charge transferred in situation 1 can be given as

$$\begin{gathered} \left|Q_1\right|=\left|\right(+6e)-(+e) \\ =5e \end{gathered}$$

Similarly, the total charge acquired by bodies during touching in pair (2) is given as

$$\begin{gathered} q_2=\frac{0e+2e}{2} \\ =\frac{+2e}{2} \\ =+e \\ \left|q_2\right|=e \end{gathered}$$

Now, the magnitude of the amount of charge transferred in situation 1 can be given as

$$\begin{gathered} \left|Q_2\right|=\left|\right(+2e)-(+e\left)\right| \\ =e \end{gathered}$$

Similarly, the total charge acquired by bodies during touching in pair (3) is given as

$$\begin{gathered} q_3=\frac{-12e+14e}{2} \\ =\frac{+2e}{2} \\ =+e \end{gathered}$$

Now, the magnitude of the amount of charge transferred in situation 1 can be given as

$$\begin{gathered} \left|Q_3\right|=\left|\right(+14e)-(+e) \\ =13e \end{gathered}$$

Hence, the rank of the pairs according to the magnitude of charges transferred by the body is$\left|Q_3\right|\ge \left|Q_1\right|\ge \left|Q_2\right|$.

b) Calculation of the rank according to the charge left on the positive charge

From calculations of part (a), we can say that the charge left over on the positively charged sphere of all the pairs is just the same charge that is acquired by each sphere.

All the positive spheres in case of the three pairs have charge equal to the value $+e.$

Hence, the ranking of the situations according to the charge left on the positive sphere isrole="math" localid="1662970981861" $q_1=q_2=q_{3.}$