Basic Concepts

In electrostatics we have seen that electric field inside a conductor reduces to zero because of motion of electrons. But if a constant potential difference is applied across a conductor (field inside the conductor is non-zero) which will force free-charges (electrons) to move.

We have seen that such movement causes charges to polarize over the surface of conductor. These induced charges set up their own electric field and make the net electric field inside the conductor equal to zero.

Now If an external path, such as wires etc. is provided to these moving charges, a current of electric charges set up.
 

Electric Current

It is defined as the rate of flow of charge through a particular area of cross section of a conductor. The direction of flow of current is always from a region of higher potential to a region of lower potential. The direction of current is opposite to direction of flow of electrons because they carry negative charge and will move from a region of higher potential. It is a scalar quantity. We define it mathematically as

Current, i = dq/dt.

Flow of electric charge constitutes electric current. For a given conductor, if ‘∂Q’ charge flows through a cross-section of area A in time ‘∂t’, then the electric current through the conductor is given as l = ∂Q / ∂t

Alt txt : current-through-conducto r

The current so defined above, is the average current over the period ∂t.

The instantaneous current is given as l = ∂Q / ∂t.

Direction of electric current as defined above will be taken along the direction of flow of positive charge, (Although in majority of conductors the charge carrier is electron which is negatively charged and hence electric current would be in a direction opposite to that of flow of electrons)

Despite the direction that we associate with electric current, electric current is not a vector quantity. Instead, we choose current density (j), that is current flowing through unit area of the cross-section, as a vector quantity.

Illustration:

A particle having charge q coulomb describes a circular orbit. If radius of the orbit is R and frequency of the orbital motion od particles is f, then find the current in the orbit.

Solution:

Through any section of the orbit, the charge passes f times inone second. Therefore, through that section, total charge pasing in one second is fq. By definition i = fq.

Illustration:

The current in a wire varies with time according to the equation | = 4 + 2t, where | is in ampere and t is in sec. Calculate the quantity of charge which has passed through a cross-section of the wire during the time t = 2 sec to t = 6 sec.

Solution:

Let dq be the change which has passed in a small interval of time dt. Then dq = | dt = (4+2t)dt

Hence, total charge passed during the interval t = 2 sec and t = 6 is

q = ∫⁶₂ (4 + 2t) dt = 48 coulomb 

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