IIT JEE / CET – Main / Advanced Physics 2013 & 2014 Electricity & Magnetism > Coulomb’s laws and Electric Feild

C O U L O U M B’ S    L A W S   &  E L E C T R I C   F E I L D

Electric charge : It’s one of the fundamental attributes of matter like mass. Could be defined as the property of some fundamental / elementary particles , by virtue of which interactions are caused between themselves and with materials they come into contact with ,  resulting in the phenomenon callede electricity. It’s an intrinsic property , in that the property exists along with the particle.Basically of two kinds – +ve charge and -ve charge.The natural unit of negative charge is that of an electron , which is equal but opposite in effect to the positive charge of the proton.

Matter in large scale , usually consists of equal numbers of electrons and protons in their atoms , and hence are electrically neutral. When there is an excess of electrons , an object becomes  negatively charged and vice – versa. If there is a flow of electrons through a body, then the flow is reffered to as electric current. Charge is measured in Coulombs and the charge of an electron is 1.602 x 10−19 couloumbs.

Charging a body –  A body becomes – vely charged when electrons are added to it , removal of electrons causes the body to become + vely charged.Protons are usually not a part of this process as they form the nucleus of atoms , and removing them from the nucleus is extremely difficult.  Eg : when a glass rod is rubbed with silk it becomes + vely charged and the silk becomes – vly charged. If an ebonite rod is rubbed with wool, it becomes -vly charged ,and hence the wool becomes +vly charged. [ Why the difference – charging a body depends on the way in which the energy levels of the electrons are distributed…i.e, whether they can be easily removed or not ].Hence if the glass rod and the ebonite rod are brought together , they will attract each other , as they involve opposite charges .

Static charge : when  the net electric charge is non-zero and motionless, the charge  is static . Even when the net charge is zero, it can be distributed non-uniformly (e.g., due to an external electric feild or to molecular motion), in which case the material is said to be polarized. The charge due to polarization is known as bound charge, while the excess charge brought from outside is called free charge.

Note A stationary charge produces an electric feild , but in non – accelerated motion , it produces both electric as well as magnetic feilds . If it is accelerating , a charges also radiates energy in the form of electromagnetic waves. )

A body can be charged by

  1. Friction –  [ the process as explained above ]
  2. Conduction – A body can be charged by an already charged body. In the case of conduction , there is a transfer of like charges . A +vly  charged body can make other bodies positively charged , but the total charges involved in the process remains the same ( more positively charged bodies n this case doesn’t mean more positive charges ) .
  3. Induction – Similar to conduction, except that there is no transfer of charges.When a charged body is brought near a neutral body, The charged body attracts opposite charges and repels like charges present in the neutral body. If the neutral body is now earthed , the like charge is neutralized by the flow of charges from the earth. In case , the earthing and the original charged body is removed , the neutral body still remains charged.
+ ve charge
- ve charge

Electric charge  – properties

  • Electric charge is quantized , i.e, charge exists in discrete packets called quanta , hence it is not a continuous spread . This means that the charge of any body is the integral multiple of the charge of an electron or proton. Q  =  ± ne , where n = 0, 1, 2, ….
  • Electric charge is conserved – The total charge of an isolated system is always constant. Note that this doesn’t mean that the positive or negative charges have to exist separately.
  • Electric charge is additive Total charge of a body is the algebraic sum of all the charges located in the body. When adding charges follow their signs , i.e,  -3C + 7C – 2C = 2 C.  [ This indicates that charge is a scalar quantity ]
  • Electric charge is invariant – The charge of a body doesn’t depend on it’s speed. [ OK , Now what happens when a speeding car is brought to rest causing a great deal of rubbing / friction between the tyres and the road…. does the car become charged ? ]

Coulomb’s Law :  The force of interaction between two charged particles , regarded as point charges q1 and q2 , separated a distance r apart , is proportional to the product of the magnitude of the two charges and inversely proportional to the square of the distance between them. 

Consider two point electric charges q1 and q2 which are at rest , separated by a distance r . The force they exert on each other is given by

F = k_\mathrm{e} \frac{q_1q_2}{r^2}

Note – k is a proportionality constant called the electrostatic force constant .

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