current&current density

It covers Current And Current density topic

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 The SI unit of current is A (ampere) 1 amp is the flow of 1 C of charge per second

3. 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

4. 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/m 2 ).

5. Flow of current in conductor: A

6. 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. (Ohm's law) electric current in a conductor

7. Magnetostatics – Surface Current Density A sheet current , K (A/m 2 ) is considered to flow in an thin layer. The Biot-Savart law can also be written in terms of surface current density by replacing Id L with K dS 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

8. Magnetostatics – Volume Current Density Current and Current Densities: Linear current I (A) Surface current density K (A/m) Volume current density J (A/m 2 ) 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 Id L with J dv J (A/m 2 )

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