1. Eng. Mohamed Ossama Ashour E-mail: vert4231@gmail.com
ELC 205A:Electric and Magnetic Fields Department of Electronics and Electrical Communications Engineering
Title page
Introduced By:
Eng. Mohamed Ossama Ashour
First term 18-19

2. Agenda Introduction to Magnetostatics Current & Current Density Vector
Conduction Current Density Vector
Boundary conditions for current density
Resistance of a Conductor
Sheet 4 Problems
Contents page
ELC 205A First term 18-19
© Mohamed O. Ashour 2018

3. Introduction
Previously, we saw problems with charge at rest. Now, we will consider charges in steady motion, which is known as a steady electric current.
Steady motion means that charges move with a constant velocity (motion doesn’t vary with time).
Steady electric current is the source of the static magnetic field.
Conducting materials will also be studied, in which charge carriers are free to move under electric field action. This movement leads to two types of currents: conduction currents and convection currents.
ELC 205A First term 18-19
© Mohamed O. Ashour 2018

4. Current & Current Density Vector
Current Density Vector
ELC 205A First term 18-19
© Mohamed O. Ashour 2018

5. Conduction Current Density Vector
This relation is known as Ohm’s law, and conductors that follow this law are called ohmic conductors or isotropic lineal conductors
ELC 205A First term 18-19
© Mohamed O. Ashour 2018

6. Boundary conditions for current density
When current obliquely crosses an interface between two media with different conductivities, the current density vector changes both in direction and in magnitude.
ELC 205A First term 18-19
© Mohamed O. Ashour 2018

7. Boundary conditions for current density
Special case (The refraction of J at a lossy dielectric or conductor interface)
For Normal components:
Also, The ratio of the tangential components can be expressed as
ELC 205A First term 18-19
© Mohamed O. Ashour 2018

8. Resistance of a Conductor
Steps of solution
ELC 205A First term 18-19
© Mohamed O. Ashour 2018

9. Resistance of a Conductor
Steps of solution
Or by using the following relation:
ELC 205A First term 18-19
© Mohamed O. Ashour 2018

10. Sheet 4
ELC 205A First term 18-19
© Mohamed O. Ashour 2018

11. Sheet 4
ELC 205A First term 18-19
© Mohamed O. Ashour 2018

12. Extra Problems 1) 2) © Mohamed O. Ashour 2018
ELC 205A First term 18-19
© Mohamed O. Ashour 2018

13. Extra Problems 3)
ELC 205A First term 18-19
© Mohamed O. Ashour 2018