In this article, we shall study the concept of quantization of electric charge and the principle of conservation of electric charges.

The fact that all observable charges are always some integral multiple of elementary charge e = 1.6 × 10^-19 C is known as quantization of electric charge.

Thus q = ± ne, where n = 1, 2, 3, …..

e = 1.6 × 10^-19 C is the magnitude of the lowest possible charge which is carried by an electron and proton. The cause of the quantization of electric charge is due to the fact that when one body is rubbed with the other, an integral number of electrons are transferred. There is no scientific explanation for quantization of electric charge in electrodynamics theory and modern physics but it can be verified experimentally.

At the microscopic level, Gell-Mann and Zweig postulated that all elementary particles are built out of more elementary constituents called quarks. Protons and neutrons are made up of two types of quarks i) up quarks denoted by ‘u’ carrying charge +2e/3 and ii) down quarks denoted by ‘d’ carrying charge – e/3. According to quark model the composition of proton is (uud) carrying charge (2e/3 +2e/3 – e/3 = e) and that of neutron is (udd) carrying charge (2e/3 – e/3 – e/3 = 0). Till now the existence of quarks is not detected experimentally but their existence is proved indirectly. In future when they are detected experimentally only we have to change the definition of quantization from e to e/3. The idea of quantization will remain the same.

Coulomb is not a Practical Unit or it is Very Large Unit:

Let us consider a body giving 1 billion (10⁹) electrons per second. Let us calculate the time to create a charge of 1 C

We have q = ne

∴ Number of electrons required = n = q/e = 1/1.6 × 10^-19 = 6.25 × 10¹⁸

Time for obtaining these electrons = t = 6.25 × 10¹⁸/ 10⁹

= 6.25 × 10⁹ seconds =  6.25 × 10⁹/ (365 × 24 × 60 × 60) = 198.2 years

This indicates that the coulomb is a very large unit, hence practical units like milicoulomb (mC), microcoulomb(μC), nanocoulomb (nC) are used.

Principle of Conservation of Charges:

Electric charge can neither be created nor be destroyed but it is transferred from one part of a system to another part of the system so that the total charge of an isolated system remains constant.

Illustration – 1:

When a glass rod (electrically neutral) is rubbed with a silk cloth (electrically neutral), the loosely attached valence electrons of the glass rod get transferred to the silk cloth. Thus in case of glass rod becomes electron-deficient and acquires a positive charge, while the silk cloth has the excess of negative charge and acquires a negative charge. The total charge of the system i.e. the glass rod and the silk cloth remains zero.

Illustration – 2:

When a γ ray photon having energy equal or greater than 1.01 MeV passes near very close to the nucleus, the electric field created by the nucleus would annihilate γ rays photon and create a pair of an electron and positron. This phenomenon is known as pair production. It is represented as

γ   → e^–   +  e⁺

We can see that the total charge on either side is equal (zero)

Illustration – 3:

When electron and positron come very close to each other, they disappear forming two γ ray photons each of energy o.51 MeV. This phenomenon is known as annihilation of matter. It is represented as

e^–  + e ⁺  →  γ   +   γ

We can see that the total charge on either side is equal (zero)

Illustration – 4:

Consider the following reaction showing α decay of uranium.

₉₂U²³⁸  →  ₉₀U²³⁴  +  ₂He⁴

We can see that the total charge on either side is equal (+ 92e)

Illustration – 5: 

Consider nuclear fission reaction

₉₂U²³⁵  +  ₀n¹  → ₁₅₆Ba¹⁴¹  +  ₃₆Kr⁹²   + 3 ₀n¹ + Energy

We can see that the total charge on either side is equal (+ 92e)

Electric charges have additive nature. The total electric charge on a body is equal to the algebraic sum of all the electric charges located anywhere on the body. When doing the algebraic sum due importance should be given to the sign (positive or negative) should be given.

Numerical Problems:

Example – 01:

How much electronic charge is required to make 1 coulomb.

Given: Total charge = q = 1 C, Electronic charge = e = 1.6 × 10^-19 C

To find: Number of electronic charge = n =?

Solution:

We have q = ne

∴ n = q/e = 1/1.6 × 10^-19 = 6.25 × 10¹⁸

Ans: Number of electronic charge is 6.25 × 10¹⁸

Example – 02:

How many electrons should be removed from a conductor so that it acquires a positive charge of 3.5 μC.

Given: Total charge = q = 3.5 μC = 3.5 × 10^-6 C, Magnitude of the charge on electron = e = 1.6 × 10^-19 C

To find: Number of electrons removed = n =?

Solution:

We have q = ne

∴ n = q/e = 3.5 × 10^-6/1.6 × 10^-19 = 2.1875 × 10¹³

Ans: Number of electrons removed is 2.1875 × 10¹³

Example – 03:

Calculate the positive charge and negative charge on the water in a cup holding 250 g of water.

Given: Mass of water

To find: Number of electrons = n =?

Solution:

The molecular formula for water is H₂O. Its molecular mass is 18 g mol^-1

Number of Moles of water = Given mass/molecular mass = 250 /18 = 13.89

1 mol of   water contains 6.022 × 10²³ molecules of water

Number of molecules in 13.89 moles of water = 13.89 × 6.022 × 10²³

Number of molecules in 13.89 moles of water = 83.66 × 10²³

Each molecule of water contains 2 hydrogens (1 electron each) and 1 oxygen (8 electrons)

Number of electrons in each water molecule = 1 × 2 + 8 × 1 = 10

Total number of electrons in a cup = 83.66 × 10²³ × 10 = 83.66 × 10²⁴

Total negative charge on water = 83.66 × 10²⁴ × 1.6 × 10^-19 =1.34 × 10⁷ C

As water is electrically neutral, total positive charge=1.34 × 10⁷ C

Ans: The total negative charge is – 1.34 × 10⁷ C and the total positive charge is + 1.34  × 10⁷ C

Example – 04:

Find the number of electrons moving through an electric bulb per second, rated with power 100 W at 230 V.

Given: Power of bulb = P = 100 W, Voltage = V = 230 V

To find: Number of electrons passed = n =?

Solution:

P = VI =V q/t

∴ q = P t /V = (100 × 1)/230 = 0.4348 C

∴ n = q/e = 0.4348/1.6 × 10^-19 = 2.72 × 10¹⁸

Ans: Number of electrons passed is 2.72 × 10¹⁸

Example – 05:

Two identical spheres carrying charges -2 μC and 14 μC are made to contact each other and then separated. Find charge on each sphere after separation

Given: Charge on first sphere q₁ = -2 μC, Charge on the second sphere = q₂ = 14 μC

To find: Charge on each sphere =?

Solution:

Total charge on the system = -2 + 14 = 12 μC

As the two spheres are identical the charge will get equally distributed among them

Hence charge on each sphere = 12/2 =6 μC

Science > Physics > Electrostatics > Quantization of Electric Charge

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In this article, we shall study methods of charging of body and different apparatus used for detection of charge on the body.

Charging of Body:

Charging by Friction:

When a body is rubbed to another, there is a transfer of electrons from one body to another due to friction.  The body losing electrons is positively charged and the body gaining electrons is negatively charged. The amount of gained and the lost electrons is equal to each other. Hence the total charge of the system is conserved.

When a glass rod is rubbed with a silk cloth, the glass loses electrons and gets positively charged while the silk cloth gains electrons and gets negatively charged.

Charge Producers:

The charge producers consist of two wands, one with dark coloured material and one with white coloured material attached to a conductive disk. After rubbing the dark and white surfaces of the two charge producers together. The disk with the white surface will acquire a positive charge; the disk with the dark surface will acquire a negative charge.

Charging by Conduction:

In the electrically neutral body, there are equal numbers of electrons and protons. The body can be charged by changing this balance by some external agency.

When a negatively charged rod touches the neutral body mounted on an insulating stand, then some of the electrons from the rod pass to the neutral body. As a result, the neutral body is negatively charged by contact due to the conduction of electrons from the negatively charged rod to the neutral body.

If the rod is positively charged, then some of the electrons from the neutral body pass to the rod and the neutral body becomes electron-deficient and acquires a positive charge by contact due to the conduction of electrons from the neutral body to the positively charged rod.

When a charged object touches to a neutral object, they both have the same charge. after contact, they start repelling each other due to the same nature of the charge. When two charged bodies touch each other, the total charge of the system is conserved and they share the total charge according to their capacities.

Charging by Induction:

Conductors can also be charged without contact. Let us consider a negatively charged rod is brought near (without contact) a neutral body mounted on an insulating stand, which is a good conductor of electricity. The rod repels the electrons in the conductors. Hence electrons move towards the far end and protons stay at near end Thus, the near end acquires positive charge while the far end acquires a negative charge. The total charge is zero. Now the far end is grounded. The negative charge on the far end is a free charge it moves towards the earth, while the positive charge is a bound charge remains on the body. Now earthing is removed at the negatively charged rod moved away, the body retains the positive charge.

Let us consider a positively charged rod is brought near (without contact) a neutral body mounted on an insulating stand, which is a good conductor of electricity.The rod attracts the electrons in the conductors. Hence electrons move towards the near end and protons stay at the far end Thus, the near end acquires negative charge while the far end acquires a positive charge. The total charge is zero. Now the far end is grounded. The positive charge on the far end is a free charge it is neutralized, while the negative charge is a bound charge remains on the body. Now earthing is removed at the negatively charged rod moved away, the body retains the negative charge.

Detection of Charge on a Body:

Proof Plane:

A proof plane is used for detection of charge. If the size of a body to be tested is very large, then an instrument called proof plane is used. The proof plane is brass or an aluminium-covered conductive disk attached to an insulated handle. It is used to carry the sample of the charge on charged conductive surfaces to transfer to the electroscope.

To collect a sample, the proof plane is rested on the surface of a charged body. When the proof plane is detached it carries the same nature of charge as that carried by the charged body.

Gold Leaf Electroscope:

This instrument is used for the detection of charge and measuring static electricity. It works on the principle that the like charges repel each other.

It consists of an evacuated glass jar placed on a nonconducting surface like wood. The mouth of the jar is sealed. A brass rod passes through the seal. inside the jar, at the lower end of the brass rod, two flattened gold foils are fixed parallel to each other. Sometimes only one gold foil is fixed and thin brass plate at the lower end of the brass rod acts as a parallel plate. At the bottom and lower lateral sides of the jar, tin foils are fixed (optional), which help the gold foils to retain their charge for a longer time.  A brass disc is provided at the top of the brass rod.

When a charge is put on the disc at the top it spreads down to the plate and the gold leaves. Now both the leaves and plate will have the same charge. Similar charges repel each other and hence the leaves diverge from each other. Bigger the charge the more is the divergence of the leaves.

After the use of electroscope, the gold leaves can be made to come together by touching the disc or earthing the disc of the electroscope.

The electroscope can be charged in two ways: (a) by contact – a charged rod is touched on the surface of the disc and some of the charges are transferred to the electroscope. This is not a very effective method of charging the electroscope. or (b) by induction – a charged rod is brought up to the disc and then the electroscope is earthed, the rod is then removed. The two methods give the gold leaf opposite charges.

Pith Ball Electroscope:

A pith ball electroscope is a pith ball hanging from a copper hook by help pf a silk thread. It is used to test whether an object is charged or not.

When a non-charged object is brought near a non-charged pith ball electroscope, the pith ball will not move. If the object is charged then the pith ball will move towards the charged object because it is attracted to it.  Now both the pith ball and charged object has same nature of charge hence the pith ball moves away from the charged object. Now if the oppositely charged body is brought near the pith ball it gets attracted. The extent of repulsion or attraction depends on the strength of a charge on the charged body.

Science > Physics > Electrostatics > Charging a Body and Detection of Charge

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