JEE Main & Advanced Physics Electrostatics & Capacitance Electric Charge

(1) Charge is the property associated with matter due to which it produces and experiences electrical and magnetic effects.

(2) It is known that every atom is electrically neutral, containing as many electrons as the number of protons in the nucleus.

(3) Charged particles can be created by disturbing neutrality of an atom. Loss of electrons gives positive charge (as then\[{{n}_{p}}>{{n}_{e}}\]) and gain of electrons gives negative charge (as then \[{{n}_{e}}>{{n}_{p}}\]) to a particle. In charging mass of the body  changes as shown below

(4) Charges with the same electrical sign repel each other, and charges with opposite electrical sign attract each other.

(5) Unit and dimensional formula

S.I. unit of charge is Ampere \[\times \]  sec = coulomb (C), smaller S.I. units are \[mC,\,\,\mu C\].

C.G.S. unit of charge is Stat coulomb or e.s.u. Electromagnetic unit of charge is ab coulomb

\[1C=3\times {{10}^{9}}\,stat\,coulomb=\frac{1}{10}\,ab\,coulomb\,\].

Dimensional formula \[[Q]=\left[ AT \right]\]

(6) Charge is

(7) Electric charge produces electric field \[(\overrightarrow{E})\], magnetic field \[(\overrightarrow{B})\] and electromagnetic radiations.

(8) Point charge : A finite size body may behave like a point charge if it produces an inverse square electric field. For example an isolated charged sphere behave like a point charge at very large distance as well as very small distance close to it's surface.

(9) Charge on a conductor : Charge given to a conductor always resides on it's outer surface. This is why a solid and hollow conducting sphere of same outer radius will hold maximum equal charge. 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., \[\sigma \propto \] \[\left( 1/R \right)\]. This is why charge leaks from sharp points.

(10) Charge distribution : It may be of two types

(i) Discrete distribution of charge : A system consisting of ultimate individual charges.

(ii) Continuous distribution of charge : An amount of charge distribute uniformly or non-uniformly on a body. It is of following three types

(a) Line charge distribution : Charge on a line e.g. charged straight wire, circular charged ring etc.

\[\lambda =\frac{\text{Charge}}{\text{Length}}=\]Linear charge density

S.I. unit is \[\frac{C}{m}\]

Dimension is \[[{{L}^{-1}}TA]\]

(b) Surface charge distribution : Charge distributed on a surface e.g. plane sheet of charge, conducting sphere, conducting cylinder of

\[\sigma =\frac{\text{Charge}}{\text{Area}}=\] Surface charge density

 S.I. unit is \[\frac{C}{{{m}^{2}}}\]               

Dimension is \[[{{L}^{-2}}TA]\]

(c) Volume charge density : Charge distributes through out the volume of the body e.g. charge on a dielectric sphere etc.

\[\rho =\frac{\text{Charge}}{\text{Volume}}=\]Volume charge density                

S.I. unit is \[\frac{C}{{{m}^{3}}}\]                 

Dimension is \[[{{L}^{-3}}TA]\]

(11) Quantization of charge : If the charge of an electron \[(=1.6\times {{10}^{-19}}C)\] is taken as elementary unit i.e. quanta of charge, the charge on any body will be some integral multiple of e i.e.,

\[Q=\pm \,\,ne\] with \[n=1,\,2,\,3\,....\]

Charge on a body can never be\[\pm \frac{2}{3}e,\,\pm 17.2e\] or \[\pm {{10}^{-5}}\,e\] etc.

(12) 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 below

Charge v/s mass