Electrostatics For Pre Medical Entrance Examination NEET (স্থিরতড়িৎ) || PART: 1

✿ ELECTRIC CHARGE Charge is the property associated with matter due to which it produces and experiences electrical and magnetic effects. The excess or deficiency of electrons in a body is the cause of net charge on a body.

✿ ORIGIN OF ELECTRIC CHARGE
It is known that every atom is electrically neutral, containing as many electrons as the number of protons in the nucleus. Charge particle or charge body can be created by disturbing neutrality of an atom. Loss of electron gives positive charge (as then \({n_p}\rangle {n_e}\)) and gain of electrons gives negative charge (as then \({n_e}\rangle {n_p}\)) to a particle. When an object is negatively charged it gains electrons and therefore its mass increases negligibly. Similarly, on charging a body with positive electricity its mass decreases. Change in mass of object is equal to \(n \times {m_e}\). Where, \(n\) is the number of electrons transferred and \({m_e}\) is the mass of electron equals to \(9.1 \times {10^{ - 31}}kg\).

✿ TYPES OF CHARGE
(1) Positive Charge: It is the deficiency of electrons as compared to protons.
(2) Negative Charge: It is the excess of electrons as compared to protons.
Clarge with same electrical sign repel each other, and charges with opposite electrical sign attract each other.

UNIT AND DIMENSION OF ELECTRICAL CHARGE
Rate of flow of electric charge is called electric current i.e., \(i = \frac{{dQ}}{{dt}}\)
Or, \(dQ = idt\)

✿ S.I. unit S.I. Unit of charge is: \(Ampere \times \sec = coulomb(C)\)

✿ Some Smaller S.I. Units
milli-coulomb: \(1mC = {10^{ - 3}}C\)
Micro-coulomb: \(1\mu C = {10^{ - 6}}C\)
Nano-coulomb: \(1nC = {10^{ - 9}}C\)

✿ C.G.S System
In C.G.S system, the unit of charge is: Stat-coulomb or e.s.u of charge.

In Electromagnetic unit of charge is: absolute-coulomb.

✿ Practical Unit of Charge:
\(amp \times hour\) And faraday
\(1amp - hour = 1amp \times 3600\sec = 3600C\)
\(1faraday = 96500C\)

✿ Their mutual relation:
\(1C = 3 \times {10^9}stat - coulomb = \frac{1}{{10}}absolute - coulomb\)
Or, \(1C = 3 \times {10^9}e.s.u = \frac{1}{{10}}e.m.u\)

✿ DIMENSIONAL FORMULA OF CHARGE
As, \(dQ = idt\)
Therefore, \(\left[ Q \right] = \left[ {AT} \right]\)

NOTE:
✤ Benjamin Franklin was the first to assign positive and negative sign of charge.
✤ Franklin (e.s.u of charge) is the smallest unit of charge while faraday is largest (\(1faraday = 96500C\)).
✤ Milikan determined quanta of charge and estimated it to be equal to charge of electron.
✤ Charge of fundamental particles (i.e., electron, proton etc.) is their internal characteristics while charge on a body depends on the number of protons and electrons inside the body.
✤ The e.s.u of charge is also called stat-coulomb or Franklin (Fr) and is related to e.m.u of charge through the relation \(\frac{{e.m.u - of - charg e}}{{e.s.u - of - charg e}} = 3 \times {10^{10}}\)

PROPERTIES OF CHARGE:
✿ Charge is a scalar quantity:
Electric charge is a scalar quantity. It represents excess or deficiency of electrons.

✿ Charge is Transferable:
If a charge body put in contact with an uncharged body, uncharged body becomes charged due to transfer of electrons from one body to the another body.

✿ Charge is associated with mass:
Charge cannot exist without mass though mass can exist without charge.
✤ So the presence of charge itself is a convincing proof of existence of mass.
✤ The mass of a body changes after being charged.
✤ When a body is given a positive charge, its mass decreases.
✤ When a body is given a negative charge, its mass increases.

✿ CHARGE IS QUANTISED
When a physical quantity can have only discrete value rather than any value, the quantity is said to be quantised. The smallest charge that can exist in nature is the charge of an electron. If the charge of an electron (\( = 1.6 \times {10^{ - 19}}C\)) is taken as elementary unit i.e., quanta of charge on any body will be some integral multiple of \(e\). i.e., the quantization of electric charge is the property by virtue of which all free charge are integral multiple of a basic unit of charge represented by \(e\) . Thus charge \(q\) of a body is always given by
\(q = ne\) where, \(n\) is the positive or negative integer.
The quantum of charge is the charge that an electron or proton carries. The charge on a proton = (-) charge on an electron = \(1.6 \times {10^{ - 19}}C\).
Charged on a body can never be \( + \frac{2}{3}e\), \( \pm 17.2e\), \( \pm {10^3}e\)

🔵 NOTE:
◉ Recently it has been discovered that elementary particles such as proton or neutron are composed of quarks having charge \( \pm \frac{1}{3}e\) and \( \pm \frac{2}{3}e\). However, as quarks do not exist in free state, the quanta of charge is still \(e\).
◉ Quantisation of charge implies that there is a maximum permissible magnitude of charge.

✿CHARGED IS CONSERVED
In an isolated system, total charge does not change with time though individual charge may change, i.e., charge can neither be created nor destroyed. Conservation of charge is also found to hold good in all type of reactions either chemical (atomic) or nuclear. No exceptions to the rule have ever been found. As an example,
In a radioactive decay the uranium nucleus, (charge = +92e) is converted into a thorium nucleus (charge = +90e) and emits an alpha particle (charge = +2e)
\(U_{92}^{238} \to Th_{90}^{234} + \alpha _2^4\)

✿CHARGE IS INVARIENT:
Charge is independent of frame of reference. i.e., charge on a body does not change whatever be its speed. The numerical value of an charge is independent of velocity. It is proved by the fact that an atom is neutral. The difference in masses on an electron and a proton suggests that electrons move much faster in an atom than protons. If the charges where dependent on velocity, the neutrality of atoms would be violated.

✿CHARGE PRODUCE ELECTRIC AND MAGNETIC FIELD:
A charged particle at rest produces only electric field in the space surrounding it. However, if the charged particle is in un-accelerated motion it produces both electric and magnetic fields. And if the motion of charged particle is accelerated is not only produces electric and magnetic fields but also radiates energy in the space surrounding the charge in the form of electromagnetic waves.

✿CHARGES RESIDES ON THE SURFACE OF THE CONDUCTOR:
Charge reside on the outer surface of a conductor because like charges repel and try to get as far away as possible from one another and stay at the farthest distance from each other which is outer surface of the conductor. This is why a solid and hollow conducting sphere of same outer radius will hold maximum equal charge and a soap bubble expands on charging.

✿CHARGE LEAKS FROM SHARP POINTS:
In case of conducting body no doubt charge resides on its outer surface, if surface is uniform the charge distributes uniformly on the surface and for irregular surface the distribution of charge, i.e., charge density is not uniform. It is maximum where the radius of curvature is minimum and vice-versa, i.e., \(\sigma \propto \frac{1}{R}\). This is why charge leaks from sharp points.

🔵 COMPARISON OF CHARGE AND MASS:

Charge	Mass
1. Electric charge can be positive, negative or zero.	1. Mass of a body is a positive quantity.

2. Charge carried by a body does not depend upon velocity of the body.
2. Mass of a body increases with its velocity as \(m = \frac{{{m_0}}}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}\), where \(c\) is the velocity of light in vaccum, \(m\) is the mass of the body moving with velocity \(v\) and \({m_0}\) is rest mass of the body.
3. Charge is quantized.
3. The quantization of mass is yet to be established.
4. Electric charge is always conserved.
4. Mass is not conserved as it can be changed into energy and vice-versa.
5. Force between charge can be attractive or repulsive, according as charges are unlike or like charges.
5. The gravitational force between two masses is always attractive.