# Electric Current

The motion or flow of charges from one region to another in a material is called electric current. The moving charges can be either positive or negative or both depending on the material in which the charges move such as metals, semiconductors, ionic solutions etc.

In metals the moving charges are electrons, in semi-conductors the moving charges are electrons and holes (vacancies that act like positive charge) and in ionic solutions the moving charges are positive and negative ions. The vast majority of current carrying materials are metals, so we focus on the conduction of charge in metals here.

If there is no electric field, there is no force that moves a charge in a particular direction and such a situation is electrostatic situation. Even in a conductor (metals) in electrostatic situation there are free electrons which randomly move in any direction in a very high speed of the order of $10^6 \text{m/s}$ but the net flow of charge in a particular direction is zero.

Do not say *flow of current* which is common to say. Current is the flow of charge and flow of current does not make any sense.

When an electric field is applied in a conductor the electrons move in the direction of electric field. The collisions with massive ions in their path causes vibration to the ions which increases temperature. The net flow of charge in a particular direction is very slow which is of the order of $10^{-4} \text{m/s}$ in comparison to the random motion of electrons.

The free electrons in metals do not instantly move from one point to another in the path but instead the actual motion or drift of electrons is very slow in comparison to the speed of random motion of electrons.

You may wonder why a light bulb glows immediately after turning a switch on if the net flow of electrons is very slow ($10^{-4} \text{m/s}$). The electric field is established immediately with nearly the speed of light which applies force on all free electrons in the entire circuit, so even if the electrons move very slowly, all electrons in the circuit start to move as soon as the electric field is established.

## Direction of Electric Current

The direction of electric current is the direction of flow of charge. Positive charges move in the direction of electric field and negative charges move in the opposite direction of electric field. The positive and negative charges move in different directions but we consider the direction of electric current to be the direction of the flow of positive charge.

In Figure 1 the moving charges are positive which move in the direction of electric field but in Figure 2 the moving charges are negative moving in the opposite direction of electric field.

In Figure 2 the negative charges move in the opposite direction of electric field. If those were positive charges instead of negative charges, they would move in the direction of electric field. The direction of electric current is the direction of flow of positive charge which is the direction of electric field.

CONVENTIONAL CURRENT: The direction of electric current is the direction of flow of positive charge in a current-carrying material. This convention for the direction of electric current is called conventional current.

If the moving charges are negative, the direction of electric current is not the same as the actual direction of motion of charges but the direction of electric current has little importance which you'll notice many times. You'll see that the charge flows from lower to higher potential energy within a source of emf, so the direction of electric current within the source of emf is opposite to the direction of electric field.

If there is a net flow of charge through a cross-sectional area in a time interval, the current is the charge flowed per unit time. If $dQ$ is the charge that moves through a cross-sectional area in a time interval $dt$, the electric current $I$ is

\[I = \frac{dQ}{dt}\]

The SI unit of current is Ampere denoted by $A$ which is one column per second.

Electric current is not a vector! We are talking about the direction of electric current but it is not a vector. We are simply talking about the direction of flow of charge. The charge can move in a current-carrying material which can be both a curve or straight-line depending on the shape of the current-carrying material. For a curved wire, the charges flow in the curve. The direction of electric current is only in our words that is there is no specific direction associated with electric current like that with a vector! An electric current can be given a positive or negative sign considering the sense of direction in a loop, that is clockwise or anticlockwise in an electric circuit loop.

We can consider an analogy between the flow of charges in a conductor and flow of water in a pipe. The rate of flow of water is the same no matter whether the cross-section of the pipe is larger or smaller. Similarly, the electric current is also the same at all points in a circuit.

## Electric current, Drift Velocity and Current Density

Electric current can be described in terms of drift velocity. Most of the work done by an electric field is spent on increasing the vibration of ions in a conductor due to collisions of electrons with massive stationary ions. The motion of charges in a particular direction is not fast but instead there is a slow drift of charges along the conductor called drift velocity.

When an electric field is applied in a current-carrying material such as a conductor, there will be two things. One is the random motion of electrons due to collisions with massive stationary ions in their way and other is the slow drift of electrons in a particular direction, that is electrons also slowly cover a distance in a particular direction instead of coming back to the starting position as in the case of random motion in electrostatic situation (no electric field).

In addition to the random motion of electrons due to the collisions with the massive ions there is a slow drift along the conductor (opposite to the direction of electric field) called drift velocity.

DRIFT VELOCITY: When an electric field is established in a current-carrying material, the charges slowly cover a distance with average speed along the material towards a particular direction called drift velocity.

In a conductor with free electrons in electrostatic situation, there is no net motion of charge. Once you apply electric field across the ends of a conductor, the electric field does work on the free electrons and they slowly drift along the conductor with average speed. Before applying any electric field across the conductor, the motion of electrons is random and cover zigzag path that does not let electrons cover a specific distance but instead they eventually come to their starting point and hence there is no electric current. Just the random motion of electrons does not mean there is electric current in the conductor. There must be a net motion along the conductor for the electric current to exist.

In Figure 3 a battery connected to an electric circuit which sets up an electric field in the wire. A segment of conductor has been exaggerated where the moving charges are electrons moving in the opposite direction of electric field. But the direction of current is along the direction of electric field, that is the same direction as the direction of the flow of positive charge.

A battery does not provide electrons to push other electrons but it establishes an electric field in a circuit which applies force on free electrons in the circuit.

We consider $n$ to be the number of charged particles per unit volume (concentration of charged particle), $v_d$ be the magnitude of drift velocity of the charged particles flowing in a conductor of cross-sectional area $A$. In a time interval $dt$, the total number of charged particles flowed is $nAv_ddt$. If $q$ is the charge of one particle, the total charge flowed in $dt$ is $dQ = qnAv_ddt$. Therefore the electric current $I$ is

\[I = \frac{dQ}{dt} = n|q|Av_d \label{1} \tag{1}\]

The direction of current is the same whether the charge is positive or negative, so we replaced $q$ with the absolute value $|q|$ in the above equation. The current is the product of the concentration of charged particles, the magnitude of charge of a particle, cross-sectional area and the magnitude of drift velocity.

The current per unit cross-sectional area is called current density denoted by J:

\[J = \frac{I}{A} = n|q|v_d \label{2} \tag{2}\]

The magnitude of current density above also does not depend on the sign of charge but the current density vector does, that is

\[\vec J = nq\vec v_d \label{3} \tag{3}\]

If $q$ is negative, the direction of $\vec v_d$ is opposite to the direction of electric field $\vec E$. If $q$ is positive, the direction of $\vec v_d$ is in the direction of electric field $\vec E$. In either case the direction of $\vec J$ is the same as the direction of electric field.

Current is not a vector but current density is a vector quantity. Current simply describes the flow of charge per unit time at any point in a conductor but current density determines the current at a particular cross-sectional area, that is it describes the current at a specific point in a conductor and also tells us the direction at that point. The current is the same at all points in a circuit even if the wire has varying cross-sections but current density is obviously not.

In case of electrical wires, we can easily describe flow of charge by electric current but charges do not always flow in a predefined path. In electrolytes or more complex situations, the current density comes in handy which describes the flow of charge through a specific area; current density at a specific point represents both the direction of current (the direction of electric field) and magnitude as current per unit area at that point.

The important equation we have to describe electric current for all cases (current can either be in a predifined path or in more complex situations such as plasmas, electrolytes etc.) is Equation \eqref{3}. Different concentrations of charges such as $q_1$, $ q_2$, $q_3$ etc. may move in different directions but the total current density is the the vector sum of all current densities due to each charged particles. That also lead us to understand the total current is the sum of currents due to individual charged particles.

If the moving charges are both positive and negative, the net current is the sum of the currents by positive and negative charges.

In Figure 4 below the moving charges are both positive and negative moving in opposite directions and the net current is not zero. In Figure 5 positive and negative charges are moving in the same direction and net current is zero (its like motion of neutral objects). The direction of current density is always the same as the direction of electric field regardless the type of charges. Again Equation \eqref{3} makes it clear what the net current will be.

The current whose direction always remains the same is *direct* current (DC). Battery powered appliances use direct current. There is another type of current in which the direction of current changes continuously called *alternating* current (AC). Many electrical appliances use alternating current such as refrigerators, televisions etc.