02_-electric field principle and definition.pptx

02_-electric field principle and definition.pptx

1. ELECTRIC FIELD

2. Action at a distance Consider a point charge kept at a point in space. If another point charge is placed at some distance from the first point charge, it experiences either an attractive force or repulsive force. This is called ‘action at a distance ’.

3. ELECTRIC FIELD According to Faraday, every charge in the universe creates an electric field in the surrounding space, and if another charge is brought into its field, it will interact with the electric field at that point and will experience a force. This field concept is required to explain action at a distance

4. FIELD DUE TO A POINT CHARGE Consider a source point charge q located at a point in space. Another point charge q o (test charge) is placed at some point P which is at a distance r from the charge q. The electrostatic force experienced by the charge qo due to q is given by Coulomb’s law.

5. The charge q creates an electric field in the surrounding space. The electric field at the point P at a distance r from the point charge q is the force experienced by a unit charge and is given by Here is the unit vector pointing from q to the point of interest P. The electric field is a vector quantity and its SI unit is Newton per Coulomb (NC -1 ).

6. Electric field of positive charges

7. Electric field of negative charges

8. Coulomb’s law in terms of electric field If the electric field at a point P is then the force experienced by the test charge qo placed at the point P is , This is Coulomb’s law in terms of electric field .

9. This equation implies that the electric field is independent of the test charge q o and it depends only on the source charge q.

10. Since the electric field is a vector quantity, at every point in space, this field has unique direction and magnitude As distance increases, the electric field decreases in magnitude . The strength or magnitude of the electric field at point P is stronger than at the points Q and R because the point P is closer to the source charge.

11. Electric field due to positive charge

12. Electric field due to negative charge

13. In the definition of electric field, it is assumed that the test charge q is taken sufficiently small, so that bringing this test charge will not move the source charge. In other words, the test charge is made sufficiently small such that it will not modify the electric field of the source charge

14. This expression is valid only for point charges. For continuous and finite size charge distributions, integration techniques must be used

15. Uniform and non-uniform electric field

16. Uniform electric field will have the same direction and constant magnitude at all points in space. Non-uniform electric field will have different directions or different magnitudes or both at different points in space. The electric field created by a point charge is basically a non uniform electric field .

17. Electric field due to the system of point charges To find the electric field at some point P due to this collection of point charges, superposition principle is used. The electric field at an arbitrary point due to a collection of point charges is simply equal to the vector sum of the electric fields created by the individual point charges. This is called superposition of electric fields

18. Superposition of Electric field

19. Consider a collection of point charges located at various points in space. The total electric field at some point P due to all these n charges is given by q 1 ,q 2 ,q 3 ,------ q n

20. Electric field due to continuous charge distribution While dealing with the electric field due to a charged sphere or a charged wire etc., it is very difficult to look at individual charges in these charged bodies. Therefore, it is assumed that charge is distributed continuously on the charged bodies and the discrete nature of charges is not considered here. The electric field due to such continuous charge distributions is found by invoking the method of calculus.

21. Consider the charged object of irregular shape

22. The entire charged object is divided into a large number of charge elements q 1 ,q 2 ,q 3 ------ q n Each charge element q is taken as a point charge The electric field at a point P due to a charged object is approximately given by the sum of the fields at P due to all such charge elements

23. To incorporate the continuous distribution of charge, we take the limit In this limit, the summation in the equation becomes an integration and takes the following form Here r is the distance of the point P from the infinitesimal charge dq and r is the unit vector from dq to point P

24. Line charge distribution

25. If the charge Q is uniformly distributed along the wire of length L, then linear charge density (charge per unit length)is λ= Q/L. Its unit is coulomb per meter (Cm -1 ). The charge present in the infinitesimal length dl is dq = λdl The electric field due to the line of total charge Q is given by

26. surface charge distribution

27. If the charge Q is uniformly distributed on a surface of area A, then surface charge density (charge per unit area) is σ= Q/A Its unit is coulomb per square meter (C m -2 ). The charge present in the infinitesimal area dA is dq = σ dA The electric field due to a of total charge Q is given by

28. volume charge distribution

29. If the charge Q is uniformly distributed in a volume V, then volume charge density (charge per unit volume) is given by ρ= Q/V Its unit is coulomb per cubic meter (C m -3 ). The charge present in the infinitesimal volume element dV is dq = ρdV . The electric field due to a volume of total charge Q is given by

30. That the magnitude of the electric field is directly proportional to the mass m and inversely proportional to the charge q. It implies that, if the mass is increased by keeping the charge constant, then a strong electric field is required to stop the object from sliding. If the charge is increased by keeping the mass constant, then a weak electric field is sufficient to stop the mass from sliding down the plane. The electric field also can be expressed in terms of height and the length of the inclined surface of the plane