Electromagnetic field

1. Electro Magnetic Field
Unit-2
Prepared by
Mrs. Siva Priya. S, AP,
School of EEE,
Mar Ephraem College of Engineering, Elavuvilai

2. UNIT II ELECTROSTATICS – II
Electric potential – Electric field and equi potential plots, Uniform and
Non-Uniform field, Utilization factor – Electric field in free space,
conductors, dielectrics - Dielectric polarization –Dielectric strength -
Electric field in multiple dielectrics – Boundary conditions, Poisson’s and
Laplace’s equations, Capacitance, Energy density, Applications.

3. Electric Potential
Let an external field is present due to a point charge or charge
distribution

4. Work done
Electric field intensity is tangential to the field lines. We are moving a
point charge(+q0) from point A to B with certain restrictions
1. Charge must be moved very slowly such that at every point on the
path from A to B the acceleration has to be zero.
2. At every point from A to B net force on q0, has to be Zero.

5. • The field lines try to move the charge(+q0) along with its direction.
Hence an external agent is required to keep the charge move in the
desired path.
• Lets say the charge(+q0) is at point P, the force due field Fext is
along the direction of electric field, to keep the charge moving along
the desired path, the counter force due to external agent is Fagent,
which is opposite to the Fext.
Fext+Fagent=0
Fagent=-Fext=-q0.Eext

6. Work done by external agent in moving a point charge from point A to
point B.

7. The work done in moving +q0 in the external field Eext due to another
point charge or continuous charge distribution from point A to point
B will be
If ,

8. Q# Find work done by an external agent in slowly shifting a charge q=1μC in the
electric field E=10^3 i V/m from point (1,2) to (3,4).
Solution:

9. Q# q0=-10μC is carried along OP, PQ and back to O along QO is an external
electric field. i) Calculate work done by external agent along each path. Ii)
als0 in round trip.

12. Potential difference
As long as the external field doesn’t change,
1) Potential difference between A to B
2) Potential of point B with respect to point A
3) Potential difference between final point and initial point

13. Potential difference
dl is along path AB
Let external electric field is 1-D

14. Potential difference in external electric
field produced by point charge

16. • Charge present at P, Field lines try to take
charge q0 along with its direction. Hence

17. Field lines to force the charge to move Eext
direction.
At every point from A to B net the acceleration is
zero.
If the cahrge present at P, hat about field lines?
Field lines try to ch rge o is diet ato B along
this line
P oint, if th charfe is presnt

32. Non-ionizing and ionizing emf

33. Using Gauss’s law calculate the E due
to infinitely large uniformly charged
plate

34. • Four concentrated charges are located at the
vertices of a rectangular plane. Find the
magnitude and direction of resultant force on
Q1. Q1=0.2 C, Q2= -0.1 C, Q3= -0.2 C and
Q4=0.2 C.

35. • State and verify divergence theorem for the
vector taken over the cube x=0, x=1, y=0, y=1,
z=0, z=1.
• Example 1.39

36. • Example 1.33

37. • Three concentrated charges of 0.25μC are
located at the vertices of an equilateral
triangle of 10 cm side. Calculate the
magnitude and direction of the force on one
charge due to other two charges.
• example 1.47

38. • Calculate the electric field intensity at P(3,-
4,2) in free space.
• Q1=2 μC at (0,0,0)
• Q2=3 μC at (-1,2,3)
• Q1=2 μC at (0,0,0) and Q2=3 μC at (-1,2,3)

39. • Prove the identity
• Example 1.21