Electrostatics - Charge Conservation

Charge Conservation

Conservation of charge is the property by virtue of which total charge of an isolated system always remains constant. Within an isolated system consisting of many charged bodies charges may get redistributed due to interactions among the bodies but the total charge of the system shall remain the same.

For example, when we rub two bodies, what one body gains in charge, the other body loses the same charge. Thus it is not possible to create or destroy net charge carried by any isolated system.

However, charge carrying particles may be created or destroyed in a process. For example, a neutron turns into a proton and an electron. The proton and electron thus created have equal and opposite charge. The total charge is zero before and after the creation. Thus charges can be created or destroyed in equal and unlike pairs only.

Following examples illustrate the property of conservation of charge.
    
In the phenomenon of pair production a y ray photon materializes in to an electron and a positron having total charge – e + e = 0, which is the initial charge on a photon.

Y = e^- + e ^– (pair production)
    
In annihilation of matter, an electron and a positron annihilate eachother to produce two y – rat photons. Charge is thus conserved.

e ^- + e⁺ = y + y (annihilation)
    
In all nuclear transformations, charge number is always conserved.

For example, in radioactive decay of U – 238, the nucleus is transformed into Th – 234 with the emission of an alpha particle which is helium nucleic 

₉₂U²³⁸ ---> ₉₀Th²³⁴ + 2He4 (radioactive decay)

Note that in applying the conservation of charge principle we must add the changes algebraically with regard to their signs.

Comparison of charge and mass

We are familiar with role of mass in gravitation, and we have just studied some features of electric charge. We can compare the two as shown in table:

Charge	Mass
Electric charge on a body may be positive negative or zero.	Mass of a body is a positive quantity.
Charge carried by a body does not depend upon velocity of the body.	Mass of a body increases with its velocity as m = m0 / 1 – v2 / c2where c is velocity of light in vacuum, m is the mass of the body moving with velocity v and mo is rest mass of the body.
Charge is quantized	The quantization of mass is yet to be established.
Electric charge is always conserved.	Mass is not conserved as it can be changed into energy and vice-versa.
Force between charges cane attractive or repulsive according as charges are unlike or like charges.	The gravitational force between two masses is always attractive.

Form (1), the magnitude of force is 

F = 1 / 4π?₀ |q₁ | | q₂ | / r²

Units, dimensions and value of ?o

From (3), ∈₀ = 1 / 4πF q₁ q₂ / r²

As SI unit of charge is coulomb (C) therefore,

Units of ∈₀ = 1 / N C.C / m² = C₂ N ^{– 1} m^-2

Dimensions of ∈₀ = (AT) (AT) / (MLT^-2) (L²) = [M ^{– 1} L ^-3 T4 A²]

From (2) k = 1 / 4π ∈₀, ∈₀ = 1 / 4π K

∴ ∈₀ = 1 / 4πk = 1 / 4 x 3. 14 x 9 x 10⁹

∈₀ = 8.85 x 10^-12 C² N^-1 m^-2

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