Advertisements
Advertisements
Question
(a) Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by
`(vec"E"_2 - vec"E"_1).hat"n" = sigma/in_0`
Where `hat"n"` is a unit vector normal to the surface at a point and σ is the surface charge density at that point. (The direction of `hat"n"` is from side 1 to side 2.) Hence show that just outside a conductor, the electric field is σ `hat"n"/in_0`
(b) Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another.
[Hint: For (a), use Gauss’s law. For, (b) use the fact that work done by electrostatic field on a closed loop is zero.]
Advertisements
Solution
(a) Electric field on one side of a charged body is E1 and electric field on the other side of the same body is E2. If infinite plane charged body has a uniform thickness, then electric field due to one surface of the charged body is given by,
`vec"E"_1 = -sigma/(2in_0)hat"n"` ..........(1)
Where,
`hat"n"` = Unit vector normal to the surface at a point
σ = Surface charge density at that point
Electric field due to the other surface of the charged body,
`vec"E"_2 = sigma/(2in_0)hat"n"` ........(2)
Electric field at any point due to the two surfaces,
`vec"E"_2 - vec"E"_1 = sigma/(2in_0)hat"n" + sigma/(2in_0)hat"n" = sigma/(in_0)hat"n"`
`(vec"E"_2 - vec"E"_1)hat"n" = sigma/in_0` ......(3)
Since inside a closed conductor, `vec"E"_1` = 0,
∴ `vec"E" = vec"E"_2 = -sigma/(2in_0)hat"n"`
Therefore, the electric field just outside the conductor is `sigma/(in_0)hat"n"`.
(b) When a charged particle is moved from one point to the other on a closed-loop, the work done by the electrostatic field is zero. Hence, the tangential component of the electrostatic field is continuous from one side of a charged surface to the other.
APPEARS IN
RELATED QUESTIONS
A 4 µF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 2 µF capacitors. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?
If Coulomb’s law involved 1/r3 dependence (instead of 1/r2), would Gauss’s law be still true?
A point charge is placed at the centre of a hollow conducting sphere of internal radius ‘r’ and outer radius ‘2r’. The ratio of the surface charge density of the inner surface to that of the outer surface will be ______.
Electric-field magnitude 'E' at points inside and outside a positively charged spherical conductor having charge Q and a radius R are ______.
If R is the radius of a spherical conductor, Vm the dielectric strength, then the maximum electric-field magnitude to which it can be raised is ______.
The electrostatic potential on the surface of a charged conducting sphere is 100V. Two statements are made in this regard S1 at any point inside the sphere, electric intensity is zero. S2 at any point inside the sphere, the electrostatic potential is 100 V. Which of the following is a correct statement?
The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is ______.
Which of the following statements is false for a perfect conductor?
A solid spherical conductor has charge +Q and radius R. It is surrounded by a solid spherical shell with charge -Q, inner radius 2R, and outer radius 3R. Which of the following statements is true?
A test charge q is made to move in the electric field of a point charge Q along two different closed paths (Figure). First path has sections along and perpendicular to lines of electric field. Second path is a rectangular loop of the same area as the first loop. How does the work done compare in the two cases?
Consider a finite insulated, uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential:
A thin spherical shell is charged by some source. The potential difference between the two points C and P (in V) shown in the figure is:
(Take `1/(4 pi epsilon_0` = 9 × 109 SI units)
