Q. 16 A3.7( 15 Votes )

Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by

Where, is a unit vector normal to the surface at a point and σ is the surface charge density at that point. (The direction of is from side 1 to side 2.) Hence show that just outside a conductor, the electric field is .

Answer :

Electric field on one side of the charged is body is E1 and the electric field on the other side of the same body be E2. If infinite plane charged body has uniform thickness then the electric field due to one surface of the body is given by,


=


Where,


= a unit vector normal to the surface at a point


σ = surface charge density at that point.


ϵ0 = permittivity of free space.


Electric field due to other surface of the charged body,


=


Electric field due to both surfaces,


- = + =


Since, Inside a closed conductor electric field s zero,


= =


Hence, the electric field just outside the conductor =


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RELATED QUESTIONS :

Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by

Where, is a unit vector normal to the surface at a point and σ is the surface charge density at that point. (The direction of is from side 1 to side 2.) Hence show that just outside a conductor, the electric field is .

NCERT - Physics Part-I

Answer the following:

(a) The top of the atmosphere is at about 400 kV with respect to the surface of the earth, corresponding to an electric field that decreases with altitude. Near the surface of the earth, the field is about 100 Vm–1. Why then do we not get an electric shock as we step out of our house into the open? (Assume the house to be a steel cage so there is no field inside!)


(b) A man fixes outside his house one evening a two metre high insulating slab carrying on its top a large aluminium sheet of area 1m2. Will he get an electric shock if he touches the metal sheet next morning?


(c) The discharging current in the atmosphere due to the small conductivity of air is known to be 1800 A on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words, what keeps the atmosphere charged?


(d) What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning?


(Hint: The earth has an electric field of about 100 Vm–1 at its surface in the downward direction, corresponding to a surface charge density = –10–9 C m–2. Due to the slight conductivity of the atmosphere up to about 50 km (beyond which it is good conductor), about + 1800 C is pumped every second into the earth as a whole. The earth, however, does not get discharged since thunderstorms and lightning occurring continually all over the globe pump an equal amount of negative charge on the earth.)

NCERT - Physics Part-I