Conservation of Charge: Definition, Formula & Examples

Conservation of charge is the principle that the total electric charge in an isolated system never changes with time in the universe or particular reaction. It comes under the three principles of charge, the other two being additivity of charge and quantization of charge. Conservation of charge means that charge is neither created nor destroyed. The charged particles can be created at a subatomic level. The particles are always created in an equal positive and negative pair so that there is a consistency in the total amount of charge created. 

Key Takeaways: Conservation of charge, Charges, Systems, Maxwell equation, Electric charge, Isolated system, Vector quantity, Scalar quantity, Current density, Volume

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What is Conservation of Charges?

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Conservation of charge refers to the total charge of an isolated system which remains unchanged with time. It states that when friction is used for charging of the bodies, there is a transfer of electric charge from one body to another. However this will not lead to the creation or destruction of charge. In other words, in an isolated system with many charged bodies, charges may get distributed due to interactions among the body but eventually it is found that the total charge of the isolated system remains conserved.

Here in the conservation of charge it must be noted that the total amount of charge conserved of an isolated system is a property that remains independent of the scalar nature of charge. A scalar quantity may not be conserved while a vector quantity can be conserved.

Conservation of Charge

Conservation of Charge Formula

The conservation of charge states that electrical charges can neither be created nor destroyed. Since it is derived from Maxwell equations it is not independent and can be written in both integral and differential forms.

Integral Form

\(\int_A\)j . da = - d/dt \(\int_V\)\(\rho d \nu\) = – d\(Q\)/dt

• j = current density
• \(\rho\) = volumetric charge density
• \(Q\) - total charge inside the volume
• A = surface area of the volume
• V = volume

Differential Form

\(\bigtriangledown . j = \frac{\partial \rho}{\partial t}\)

Conservation of Charge Formula from Ampere-Maxwell’s Law

The conservation of charge is dependent on Maxwell's equations. It can be derived from Ampere-Maxwell and Gauss’s law for electric charges:

\(\bigtriangledown \times h= j +\frac{\partial d}{\partial t}\)

Taking the divergence and using \(\bigtriangledown . d = \rho f\) and a vector identity yields

\(\bigtriangledown \times h= j +\frac{\partial d}{\partial t}\) \(\bigtriangledown . j = -\frac{\partial \rho f}{\partial t}\)

Notes that in Maxwell’s equations j  refers to the free charges density.

Also Read:

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Example of Conservation of Charge

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An object can get a negative charge or positive charge. Consider an example that you can try by yourself to understand the conservation of charge. When you take a piece of glass and rub it with silk cloth, the glass object becomes positively charged and silk becomes negatively charged so both these attract each other due to the opposite charges. In the same situation, add another silk cloth and rub it with the glass object. Both the silk cloths will repel each other because both are negatively charged. A similar situation will arise if you use two glass objects and a piece of silk cloth. In this case, both glass objects will repel each other because both are positively charged.

Also Read: Dipole in a Uniform External Field

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Law of Conservation of Charges

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The law of conservation of charge states that the net charge of an isolated system remains constant. A more detailed explanation of the law of conservation of charge is given below:

• Every object has a net neutral charge which means for each proton there is an electron to balance its charge. Therefore, in a given system there will always be the same number of electrons and protons.
• When the net charge of the system is distributed in the objects, the electrons are evenly distributed on all the objects by transferring from higher to lower polarity.
• Please note that protons cannot be involved in transfer of charges. Therefore, when an object is in neutral state, it will be positively charged when the electrons in it transfer to another body.

Also Read:

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Previous Year Questions

1. Charge density of long wire λ… [ BITSAT 2009]
2. In the given circuit, what will be the equivalent resistance between the points AA and BB ? [ JIPMER 2006]
3. How to adjust a system of three identical capacitors to get high electrostatic energy….. [ UPSEE 2016]
4. A spherically symmetric charge distribution is characterised by a charge density having the following….[JEE Main 2014]
5. the initial position the kinetic energy of the particle becomes zero when...[JEE Main 2020]
6. The electric field lines around the cylinder will look like figure given in….[JEE Main 2016]

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Things to Remember

• In the conservation of charge the charge is a conserved quantity which implies it can neither be created nor destroyed.
• The particles are always created in an equal positive and negative pair so that there is a consistency in the total amount of charge created.
• Charge can be transferred from one body to another through processes like induction or conduction.
• When we say charging an object, it involves transfer of electrons from one body to another by rubbing two bodies.