Mobility Charge Assignment Help

Electrostatics - Mobility Charge

Mobility Charge

Mobility of charge (u) responsible for current is defined as the magnitude of drift velocity of charge per unit electric field applied. 

μ = drift velcoty / electric field = vd / E  = q E τ/m / E = qτ / m 
Where τ is the relaxation time of the charge while drifting towards the opposite electrode and m is the mass of the charged particle.

Mobility of election μe = e τe / me

Mobility of holes (positive charge carriers present in semiconductors) will be given by 

μ h = e τh / mh

Where τe and τh are average relaxation time for electrons and holes respectively me and mh refer to mass of electron and whole respectively charge on either is e. 

Mobility is positive for both positive current carriers and negative current carriers; al thought their drift velocities are opposite to each other.

The congenital current in a conducting material due to motion of negative current carriers will be in the same direction as that due to positive current carriers. Therefore the total current in the conducting material is the sum of the currents due to positive current carriers and negative current carriers. 

If there are only electrons in a conducting material as current carrier then the drift velocity of electron is vd = μeE

SI unit of mobility is 

M2s -1 V-1 or ms-1 N-1 C

Mobilizes of some materials at room temperature are given in table 

Mobility of some materials

Materials Electrons mobility (cm2V-1s-1) Holes mobility (cm2V-1s-1)
Diamond 1800 1200
Silicon 1350 480
Germanium 3600 1800
InSb 800 450
GaAa 8000 300

Consider a conductor (say a copper wire) of length t and of uniform area of cross-section A.

∴ Volume of the conductor = A/

If n is the number density the number of free electrons per unit volume of the conductor, then total number of free electrons in the conductor = A in if e is the charge on each electron, then total charge on all the free electrons in the conductor, 

Q = alne

Let a constant potential difference V be applied across the ends of the conductor with the help of a batter.

The electric field set up across the conductor is given by 

E = V/I (In magnitude)

Due to this field the free electrons present in the conductor will begin to move with a drift velocity vd towards the left hand side as shown in 

∴ Time taken by the free electrons to cross the conductor t = l / vd

Hence current t = q / t = A lne / ivd

I = A n e vd

Because vd = μe E, so I = Ane μeE

In a conductor there is large number of free electrons or conduction electrons. If there is one free electron per atom the number of free electrons per cubic meter of the conductor will be of the order of 1099

When we close the circuit the electric field is set up in the entire closed circuit instantly with the speed of electromagnetic wave which causes electron drift at every portion of the circuit. Due to which the current is set up on the entire circuit instantly. The current so set up does not wait for the electrons to flow from one end of the conductor to other end. It is due to this reason, the electric bulb glows immiediately switched on. 

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