Conservation of Charge

Conservation of Electric Charge Definition

Before learning about the conservation of an electric charge, let us first discuss an electric charge. When we rub a balloon with our hair, the balloon starts attracting our hair when it's held within proximity. This is due to the electrostatic force of attraction between the charges on the hair and the balloon. On the other hand, when bringing two such balloons (that are rubbed with hair) close to each other, they start to repel each other. This is due to the electrostatic force of repulsion. These two types of behavior of the electric charge show the existence of two possible types of electric charge. One is a positive charge, and the other is a negative charge.

In line with convention, we denote the positive charge as \(+q\) and the negative charge as \(-q\). In simple words, we use the plus sign for positive charges and a minus sign for negative charges.

Fig. 2 - Two possible interactions between the electric charges due to an electrostatic force of attraction and repulsion between unlike and like charges.

The fundamental charge carriers are electrons and protons. Although the mass of the proton is 1836 times the mass of the electron, the amount of charge on either carrier is the same, i.e., \(1.6\times10^{-19}\,\mathrm{C}\), where \(\mathrm{C}\) (\(\mathrm{Coulomb}\)) is the SI unit of electric charge.

There are three fundamental properties of the electric charge,

1. Additive in nature - The net electric charge in the system is the sum of individual charges.

2. Quantization - The amount of electric charge on the substance is an integral multiple of its fundamental value, i.e., \(q=ne\) where \(n\) is an integer and \(e=1.6\times10^{-19}\,\mathrm{C}\) is the fundamental value of the charge.

3. Conservation of electric charge - The net charge in an isolated system remains conserved.

Law of Conservation of Electric Charge

In the previous example of a balloon rubbed with hair, the electron affinity of the balloon is significant. So, the electrons are transferred from the hair to the balloon, which makes the hair positively charged and the balloon negatively charged.

There is no addition of charge from any external source in the system. Therefore, the amount of negative charge on the balloon equals the positive charge on the hair.

Initially, the balloon and the hair were neutral. So, the net charge on the system in the initial state is zero.

Let \(q\) be the magnitude of the electric charge on the balloon and the hair. Then by the sign convention, \(-q\) is the charge on the balloon, and \(+q\) is the charge on the hair. The net electric charge in the system after the charging by rubbing becomes \(+q+\left(-q\right)=q-q=0\). In conclusion, the net charge on the system in the final state is the same as in the initial state, i.e., zero. This constant value of net electric charge proves the law of conservation of electric charge.

Examples of Conservation of Charge

To understand charge conservation in more detail, let us consider a few examples which involve the charging of a material while the net charge of the system remains conserved. There are three different charging methods: charging by friction, charging by induction, and charging by conduction. In this part, we will learn how the net electric charge is conserved in each charging method.

Charging by Friction

Imagine we rub a glass rod with a silk cloth. The electron affinity of the silk cloth is high. Thus, the electrons are transferred from the glass rod to the silk cloth. As a result, the glass rod becomes positively charged, and the silk rod becomes negatively charged.

Fig. 3 - Charging of silk cloth and glass rod is carried out by the method of charging by friction with the transfer of electrons from the glass rod to silk cloth.

Initially, the glass rod and the silk cloth do not have any net charge, meaning the initial charge is zero, and both objects are said to be neutrally charged.

From Fig 3, we can see that after charging by friction, the electric charge on the glass rod is \(+6e\) (with each plus symbol representing an amount of charge equal to the elementary charge), and the electric charge on the silk cloth is \(-6e\) (and the negative signs indicating an amount of charge equal to the elementary charge but with the opposite polarity). The net charge on the system in the final state becomes \(-6e+6e=0\).

In conclusion, the net electric charge in the initial state equals the net electric charge in the final state. This demonstrates the law of conservation of electric charge.

Charging by Induction

Imagine we place the initially positively charged glass rod near the uncharged metal sphere. Due to the electrostatic force of attraction, the negative charge will collect on one side of the sphere facing the rod. However, due to the electrostatic repulsion force, the positive charge will gather on the other side of the sphere.

Fig. 4 - Polarization of metal sphere due to the presence of charged glass rod in the proximity of the metal sphere.

In the initial state, the electric charge on the glass rod is \(+6e\), and the electric charge on the metal sphere is zero. Therefore, the net electric charge in the initial state is \(+6e+0=+6e\).

After the charging by induction, the electric charge on the metal sphere is \(-6e+6e=0\), and the electric charge on the glass rod is \(+6e\). So, the net electric charge in the final state is \(0+6e=+6e\). In conclusion, the net electric charge in the initial state equals the net electric charge in the final state. This example once again demonstrates the law of conservation of electric charge.

Charging by Conduction

Imagine we place a charged metal sphere in contact with an uncharged metal sphere. Then the charge transfer takes place from charged sphere to the uncharged sphere till the net charge on each sphere becomes the same.

Fig. 5 - Charging of an uncharged metal sphere due to the transfer of electric charge from the charged sphere to the uncharge sphere when both are in contact with each other.

The above figure shows that in the initial state, the electric charge on the charged metal sphere is \(+8e\). On the other hand, the electric charge on the uncharged sphere is zero. So, the net electric charge in the initial state is \(+8e+0=8e\).

The electric charge on either sphere after the charging by conduction method is \(+4e\). The net charge in the final state becomes \(+4e+4e=8e\). In conclusion, the net electric charge in the initial state equals the net electric charge in the final state. This proves the law of conservation of electric charge.

From the above discussion, it is clear that all the charging methods follow the law of conservation of electric charge.

Conservation of Electric Charge in Nuclear Reactions

Two main types of nuclear reactions are nuclear fission and nuclear fusion. The electric charge on the nucleus remains conserved during this nuclear reaction. Let's discuss this charge conservation in either type of nuclear reaction.

Nuclear Fission

Uranium-235 nuclei are some of the most well-known large unstable nuclei. When Uranium-235 is bombarded with a neutron, then the Uranium breaks into Barium-139 and Krypton-94 combined with the emission of 3 neutrons. \[\ce{^1_0n + ^235_92 U -> ^139_56 Ba + ^94_36Kr + 3 ^1_0n}\]

In the above reaction, the electric charge on the nucleus of Uranium is \(+92e\), and the electric charge on the neutron is zero. So, the net electric charge on the reactant side is \(+92e+0=+92e\).

The electric charge on the nucleus of Barium is \(+56e\), and the electric charge on the nucleus of krypton is \(+36e\). Therefore, the net electric charge on the product side is \(+56e+36e=92e\). In conclusion, the net electric charge in the system is conserved during the nuclear fission reaction.

Nuclear Fusion

For example, the unstable isotopes of hydrogen, i.e., Deuterium 2 and Tritium 3, react with each other to produce a stable Helium 4 nucleus combined with the neutron emission. \[\ce{^2_1H + ^3_1H -> ^4_2He + ^1_0n}.\]

From the above reaction, the electric charge on the nucleus of Deuterium is \(+1e\), and the electric charge on the nucleus of Tritium is\(+1e\). Therefore, the net electric charge on the reactant side is \(+1e+1e=2e\).

Similarly, the electric charge on the helium nucleus is \(+2e\), and the electric charge on the neutron is zero. So, the net electric charge on the product side is \(+2e+0=+2e\). Thus, the net electric charge on the system remains conserved in the nuclear fusion reaction.

Conservation of Electric Charge in Electric Circuits

Two electrical device arrangements (series and parallel) are possible in electric circuits. However, even though the electrical devices are arranged differently, the net electric charge in the circuit remains conserved.

In the series circuit, there is a single path of current. This is because all the electrical devices are connected along the same line from end to end.

Fig. 6 - The figure shows the flow of the same current through the electrical devices in the series circuit.

There is only one path, so the same amount of charge is passed through all the devices. This confirms the conservation of electric charge in the series circuit.

In the parallel circuit, the electrical devices are connected in parallel to each other. Therefore, the current flowing through each device varies, corresponding to the resistance across the device.

Fig. 7 - The figure shows the flow of current through the branches in the parallel circuit.

But, the net current through the circuit equals the sum of electric current through each branch is conserved. In other words, the net electric charge through any node in the circuit is conserved. This confirms the conservation of electric charge in parallel circuits.