Magnetic Field Due to a Current Element

Resistivity is the quality of a material that creates a barrier for the electric current and hampers the speed and velocity of the material. The resistivity of a material is contrarily proportional to the drift of electrons. When the electrons present in the circuit move randomly, the net velocity of a circuit becomes 0, and the field of electricity is not applied to the circuit.

What is resistance?

An electron moving via the electric wires & loads of an external circuit experienced the resistance. The resistance is the hurdle to the flow of the charge. An electron does not move in a direct route between the terminals. It follows the zigzag pattern where the electron experiences several collisions with stable atoms in the conducting material. In other words, an electron experiences numerous hindrances during its movement from one terminal to another and it is known as electrical resistance. The SI unit to measure the electrical resistance is ohms (Ω). 

To further understand the Drift of electrons and the origin of resistivity, you can assume a graph with the current (I) to the voltage (V) ratio. You will notice that the current will flow with the points A, B, and C, but this will slowly turn to a constant state after a matter of time. This is the time the resistance will start performing its work.

What is drift force?

The electrons move or drift inside a conductor due to drift force. First, you should know that the subatomic particles contain random mobility, including the electrons and other particles present in the materials. The electrons are free to move anywhere; However, in this case, they drift slowly from one point to another and move towards the electric field source. This is defined as the drift velocity present in the electrons.

However, the total forces at which the electrons perform the drift inside the conductor are defined as the drift velocity of electrons. In simple terms, it is the average force acquired by the electrons or charged particles present in an element due to the presence of an electric field. 

Furthermore, the SI unit of the drift velocity is m/s. Also, the unit of drift velocity can be represented by m2/(V.s).

The drift of electrons and the origin of resistivity

It is already clear that the free electrons move randomly from one atom to another with the help of thermal velocity. However, when the entire motion is unknown, the momentum automatically turns to 0. It is the situation when no electric field is provided.  

Furthermore, a coalition among the electrons and the atoms provides the velocity, which on average, is defined as drift velocity. 

For instance, let’s assume a conductor with V and L, where V denotes the potential difference, and L denotes the length of the conductor. 

So, E= V/L 

Here, the external electric field provides an additional influence that affects each electron’s velocity. The force of each electron will thus be F= -eE, and 

F= ma, where m is mass, and a represents acceleration. 

 Thus ma= -eE

Thus from the above equation it is found that individuals pose a different amount of acceleration that will be opposite to the direction of the field, with the formula a= -Ee/m, here, e represents the charge, m is the mass, and E is the electric field applied. With the amount of electric field used, the electrons will be more attracted towards the positive atoms and thus have a fast movement velocity. 

Furthermore, the electrons lose their velocity after colliding with the heavy, positively charged atoms. Also, they lose their capacity to move as they are heavily weighted. 

For instance, imagine the Velocity of free electrons represented by n is provided as u1+u2+u3…..u3. 

The vector sum will become 0 

However, after providing an electrical field, the electrons become V1+V2+V3….VN. 

Here V1= u1+ aԏ1 and the ԏ1 represent the time needed for collisions between the first electrons. 

Likely, V2= u2+ aԏ2,

And VN= un+ aԏn

Thus the average velocity of all the free electrons is equal to the drift velocity, or Vd. That can be denoted as:

vd= v1+v2+ v3…… vn/n, and substituting the values of the v1, v2, v3… vn, you can avail, 

vd+ (u1+ aԏ1) +(u2+ aԏ2)+…………(un+ aԏn)/n

= (u1 + u2 +…… un/n) + (aԏ1 + aԏ2 +aԏn)/n

= u1 + u2 +….. un/n +a(ԏ1 +ԏ2 +…. ԏn)/n 

=) vd= u +aԏ

Here ԏ= ԏ1 +ԏ2 +……. ԏn/ n. 

Relation between drift velocity, resistivity, and current

The current flowing per unit area, with the area being normal to current, is defined as the current density. 

Current J= I/A, where I represent the current, and A is the area, which means 

= ne A vd/ A= nevd

= ne 2ԏ E/m 

The conductivity is further represented as the σ = n e2 ԏ / m.    

Thus, J = σ E, and

Resistivity of the material= ρ = m / n e2 ԏ

Thus, vd = e V ԏ / mL, where v is the potential difference of the ends of the conductors, where, e represents charge,  ԏ is the relaxation time. And m is the mass, with L is the length. Thus, it is found that V = vd mL / e ԏ – (equation 1). 

Also, I = n e A vd, thus subtracting the value of vd it is concluded that 

V = (I / n e A) m L / e ԏ = (m L / A n e2 ԏ) I,

 can also be written as V = (m / n e2 )×(L / A )× I 

Thus V = (ρ L / A) I

Conclusion

Thus, the drift of electrons and the origin of resistivity can be considered that the drift force is the energy that drives the electrons through the conductor. The point that stops the drift force is resistivity. However, the drift of electrons and the origin of resistivity start when external electrical power is applied to the conductor. Due to this force, the electrons become negatively charged and thus get attracted toward the positive charge. The atoms further take the positive direction when the electrons go away. Thus a coalition among both the positive and negative is formed. But as the mass of the positive ions remains high, this does not move, and the electrons perform all the movements.