# Landsberg - Elementary Textbook of Physics Vol 2 - Mir - 1988

Chapter 1 Electric Charges

1.8.1 Explain the method of determining the sign of the charge on electroscope, shown in Fig. 17.

Figure 17: Determination of the sign of an unknown charge. When a like charge is brought close, the electroscope leaves diverge to a still larger angle, while when an unlike charge is brought close, the leaves collapse.

Electric charges are of two types labelled arbitrarily as negative and positive. Two fundamental facts about electric charges are that

  1. If we make contact between like and unlike charges, they neutralise each other.
  2. Like charges repel each other while unlike charges attract each other.

Let us first understand the working principle of an electroscope. The electroscope has two metal leaves which are connected to a conductor outside the bottle. The leaves are made from very thin sheets and are very light (very little mass). Because of their lightness, small forces can cause considerable deflection in them. When we charge the electroscope by touching it with a charged body, let’s say a positive (or negative) charge, both the leaves of the electroscope acquire a positive (or negative charge). Since both the leaves have the same charge (either both positive or both negative), they repel each other and hence the leaves diverge.

If we, were to increase the charge on the leaves, the divergence between the leaves will also increase as the force between the leaves increases. On the other hand ff we, were to decrease the charge on the leaves, the divergence between the leaves will also decrease as the force between the leaves increases.

Now in Figure 17, a charged rod is brought near the electroscope. This charged rod induces opposite charges on the top spherical knob (conductor) of the electroscope. For example, as shown in the figure if the charged rod is positive, it will induce negative charges on the electroscope. But if there are negative charges induced at the top, that would mean at the other end, that is in the leaves, positive charges will be induced. That means that there will be an increase in the positive charge of leaves. Now if the initial charge of the electroscope is positive, it would mean that leaves will get more positive induced charge and hence total charge on the leaves will increase and leave will diverge more. Other the other hand if the initial charge of the electroscope if negative, it would mean that the leaves will get a more positive induced charge and hence the total charge on the leaves will decrease, and hence the leaves will collapse. These two cases are depicted in the Figure 17.

1.8.2. An electroscope is charged by induction with the help of a glass rod. How will electrons be displaced in this case?

A glass rod when charged by rubbing will get a negative charge. When it is brought near an electroscope, it will induce positive charges on the ball of the electroscope. The positive charges on the ball of the electroscope would mean that the electrons will go to the other end, that is to the leaves of the electroscope.

1.8.3. A neutral metallic body is brought close to the ball of a charged electroscope, without touching it. How will the divergence of the leaves change? Explain the phenomenon.

Let us suppose that the electroscope is charged positively. In the case of charging by induction the charges induced at the far end of the neutral body has the same sign as that of the charged body, while in area near the charged body the opposite charge is induced. When a neutral metallic body is brought close to the ball of the electroscope, it will create negative induced charges (opposite to the charge on the electroscope) on the body. The induced charges are only at the ends of the body in our case the metal ball and the leaves of the electroscope. Because of this induced negative charge on the body there will be extra positive charge on the ball which means that there will be extra negative charge at the other end, namely at the leaves. Thus the total charge of the leaves will decrease and as a result their divergence will decrease.

1.8.4. A negatively charged body is brought to a positively charged electroscope. As the body approaches the electroscope, the divergence of its leaves decreases to zero. At a closer approach, however, a divergence is observed again. What processes occur in this case?

When a negatively charged body is brought near a positively charged electroscope, it will induce positive charges on the ball of the electroscope and negative charges on the leaves. This will increase the net positive charge on the ball (as both induced and original charges are positive), and will decrease the net positive charge on the leaves (as induced charges are negative and original charges are positive). At a certain stage during the approach of negatively charged body (if the charge is much greater than the charge on the electroscope), the induced negative charges will be equal to the original charges. This is the time when the divergence of the leaves becomes zero. As the negatively charged body still approaches further it will induce more negative charges in the leaves, which are greater than the original positive charges. It is due to these negative induced charges, the leaves will diverge again.

1.8.5. When a hand approaches a charged load suspended on a silk thread, the load is attracted to it. Why does this happen?

The charged load suspended on a silk thread is an insulated body. When we approach this charged body with a neutral body, such as our hand, it will induce charges on the neutral body. The induced charges on the hand will be opposite of the charged load. Due to the opposite nature of the charges, there will be an attraction between the two. Hence, the load is attracted to the hand.