The document summarizes key concepts related to electric current, current density, and magnetostatics. It defines: - Electric current as the rate of charge transfer through a surface. The SI unit is the ampere. - Conventional current direction versus actual electron flow direction in conductors. - Current density as the current per unit area, with units of amperes per square meter. It is proportional to and in the same direction as the electric field in a conductor based on Ohm's law. - Surface and volume current density and how they relate to the Biot-Savart law for calculating magnetic fields.

1. Subject:- Field Theory
Topic:-Current And Current density
Prepared By :
Dhruv Aradeshana (150110109004)
Tejas Dobariya (150110109010)
Dhruval Gondaliya (150110109011)

2. Electric current
• The electric current across a surface is defined as the rate
at which charge is transferred through this surface
I
dQ
dt

• The SI unit of current is A (ampere)
• 1 amp is the flow of 1 C of charge per second

4. Conventional current:
• Scientist first thought that positive charges flow from the positive
terminal of a cell to the negative terminal. This is called the
conventional current direction.
• However, it was found that a current in a metal wire is in fact a
flow of negatively-charged electrons in the opposite direction.
Nevertheless, the conventional current is still used.
+ – electron flow
convention
current

5. Current Density
The magnitude of current density, J, is equal to the current per unit
area through any element of cross section. It has the same direction as
the current.
If the current is uniform across the surface and parallel to dA, then J is
also uniform and parallel to dA, and then
Here, A is the total area of the surface.
The SI unit for current density is the ampere per square meter (A/m2).
  AdjI

6. Flow of current in conductor:
I
J
A
A
1
R
l




surface
AdJ

EAJA V
A

l
A
l


7. • In a conductor, current density is proportional to the
electric field vector
• The constant of proportionality  is called the conductivity
of the conductor.
• Under a steady flow of charged particles along a
conductor, the current across any cross section of the
conductor has the same value.
We assign this value to the current in the conductor.
 
J E  (Ohm's law)
electric current in a conductor

8. Magnetostatics – Surface Current Density
A sheet current, K (A/m2) is considered to flow in an thin layer.
The Biot-Savart law can also be written in terms of surface
current density by replacing IdL with K dS
2
4
RdS
R

 
K a
H
Important Note: The sheet current’s direction is given by the vector
quantity K rather than by a vector direction for dS.
Method 2: The surface current sheet problem can be treated as a sheet
consisting of a continuous series of line currents.
Line current
Method 1: The surface charge problem can be treated as a sheet
consisting of a continuous point charge distribution.
Point charge

9. Magnetostatics – Volume Current Density
Current and Current Densities:
• Linear current I (A)
• Surface current density K (A/m)
• Volume current density J (A/m2)
• For many problems involving surface current densities, and indeed
for most problems involving volume current densities, solving for
the magnetic field intensity using the Law of Biot-Savart can be
quite difficult and require numerical integration.
• For most problems that we will encounter with volume charge
densities, we will have sufficient symmetry to be able to solve for
the fields using Ampere’s Circuital Law.
The Biot-Savart law can also be written in terms of volume current
density by replacing IdL with Jdv
2
4
R
dv
R

 
J a
H
• J (A/m2)

10. Thank You…..