12P01.6_Gauss’s Law and its Applications_Final.pptx

Gauss’s Law and its Applications, Physics

1. 12P01.6 Gauss’s Law and its Applications

2. Learning Objectives Gauss’s Law Applications of Gauss’s Law 12P01.6 Gauss’s Law and its Applications

3. 12P01.6 CV 1 Gauss’s Law

4. Electric flux through a closed surface is times of charge enclosed by surface .   4 Gauss’s Law                    

5. Gauss’s Law           Important points regarding this law : Gauss’s law is true for any closed surface, no matter what its shape or size.        

6. The term on the right side of Gauss’s law equation, includes the sum of all charges enclosed by the surface . The charges may be located anywhere inside the surface.   Gauss’s Law   The electric field is due to all the charges, both inside and outside S .     For surface ,   due to all charges (          

7. The surface that is chosen for the applications of Gauss’s law is called Gaussian surface. Im portant points: We can choose any Gaussian surface and apply Gauss’s law. Gaussian Surface

8. Gaussian Surface If ,     If ,       Now if magnitude of electric field is constant, G aussian surface is choosen such that electric field is either perpendicular or parallel to the area vector of Gaussian surface and magnitude of electric field is constant at every point of Gaussian surface.         where area of surface

9. Concept Test Ready for a challenge

10. Q. A point charge is placed at the center of a half sphere. Find out the electric flux passing through the surface.   Pause the Video (Time Duration : 2 Minutes)

11. Q. A point charge is placed at the center of a half sphere. F ind out the electric flux passing through the surface. Sol.   Consider an imaginary upper hemisphere so that the charge 𝑞 is now enclosed within a sphere. Now, the charge is symmetrically located with respect to both the hemispheres.   Thus,   By Gauss’s Law, Flux through the entire sphere     ∴Flux through the lower hemisphere    

12. Concept Test Ready for a challenge

13. Q. Electric charges are distributed in a small volume. The flux of the electric field through a spherical surface of radius surrounding the total charge is . What will be the flux over a concentric sphere of radius ?   Pause the Video (Time Duration : 1 Minutes)

14. Q. Electric charges are distributed in a small volume. The flux of the electric field through a spherical surface of radius surrounding the total charge is . What will be the flux over a concentric sphere of radius ?               The net charge enclosed by the larger concentric sphere is the same as that enclosed by the smaller sphere. By Gauss’s law, So, electric flux remains the same, 𝑖.𝑒.   Sol.

15. 1 2P01.6 PSV 1

16. Q. Find the flux passing through a cube, if charge is placed (a) A t the center of cube (b) At a face of cube (c) At a corner of cub e   (a) F lux passing through cube   Sol.  

17. These cubes makes a cuboid. And flux passing through this cuboid       Sol. When charge is placed at the face of cube.   So, flux passing through one cub e charge will be shared by cubes.   Thus, flux passing through every cube will be same.  

18. Sol. Charge will be shared by cubes.      

19. Sol.     Charge will be shared by cubes.   These cubes makes a big cube. And flux passing this cube   Thus, flux passing through every cube will be same. So, flux passing through one cub e    

20. 12P01.6 CV 2 Applications of Gauss’s Law

21. Electric field due to an infinitely long straight uniformly charged wire  

22.                     Electric field due to an infinitely long straight uniformly charged wire     will be in horizontal direction.   Take two elements at distance from mid point ,   Charge of element   Thus , electric field for every element will be in horizontal direction. So we can say electric field due to infinitely long straight wire will be radial for every point.              

23. Electric field lines for an infinitely long straight uniformly charged wire

24. Gaussian surface

25. At the cylindrical part of the Gaussian surface,   Electric field due to an infinitely long straight uniformly charged wire   r l Take a cylindrical Gaussian surface, coaxial with the wire, of radius and length .   E r P Total electric field at any point is radial.       Now , from Gauss’s law     Direction of electric field will be directed outward if is positive and inward if is negative.          

26. Concept Test Ready for a challenge

27. Q. An infinitely long wire is uniformly charged which charge density is . Find out the electric field at a distnce of from wire.   Pause the Video (Time Duration : 1 Minutes)

28. Q. An infinitely long wire is uniformly charged which charge density is . Find out the electric field at a distnce of from wire.   Sol.   Direction of electric field will be directed outward.

29. Electric field due to a infinitely uniformly charged infinite plane sheet Surface charge density s We can consider infinite plane sheet is made of infinite straight long wires. We know electric field due to infinite straight long wire is radial at every point. So electric field due to infinite plane sheet will be also radial.

30. Electric field lines due to a infinitely uniformly charged infinite plane sheet

31. Electric field due to a infinitely uniformly charged infinite plane sheet Surface charge density s Take a rectangular parallelopiped Gaussian surface of cross sectional area .   Now, from Gauss’s law   Electric field is directed away from the plate if is positive and towards the plate if is negative.   x x For other surfaces,   E E     1 2 z x y

32. Electric field due to a uniformly charged thin spherical shell      

33. Electric field lines due to a uniformly charged thin spherical shell

34. Field outside the shell   Electric field due to a uniformly charged thin spherical shell

35. Field outside the shell         Electric field due to a uniformly charged thin spherical shell       Where is the total charge on spherical shell   The electric field is directed outward if and inward if .            

36.       Field inside the shell                 For gaussian surface 1 Similarly for gaussian surface 2       Electric field will be zero everywhere inside the uniformly charged thin spherical shell.

37. Summary Electric flux through a closed surface is times of charge enclosed by surface . Electric field due to an infinitely long straight uniformly charged wire, Electric field due to a infinitely uniformly charged infinite plane sheet Electric field due to a uniformly charged thin spherical shell For outside the cell, For inside the cell,        

38. Reference Questions NCERT : 1.17, 1.18, 1.19, 1.20, 1.23, 1.24 Work Book : 4, 5, 12, 15, 16, 17, 19 38 Gauss’s Law and its Applications