Derive the expression for the relation between drift velocity and electric current
Answers
In a conductor, there are large number of free electrons. When we close the circuit, the electric field is established in the circuit with the speed of electromagnetic wave which causes electron drift at every portion of the circuit. Due to which the current is set up in the entire circuit instantly. The current thus set up does not wait for the electrons to flow from one end of the conductor to another end. It is due to this reason, the electric bulb glows immediately when the switch is on.
Answer:
Allow us to consider a conductor of cross sectional area A. The volume element for a length Δx is AΔx.
If n is the number of electrons according to unit volume, the number of electrons in this volume element can be n*AΔx. The overall charge in this volume element is Δq=n*AΔx*e, in which e is charge on the electron.
If electrons drift with a velocity vd because of thermal strength, the space traveled in time Δt is Δx=vd*Δt.
On substituting this value of Δx within the expression for Δq, we discover that total charge within the volume element below consideration is given by means of;
Δq=n*A*e*vd*Δt
After modification;
Current I= Δq/Δt= n*A*e*vd