Establish the relation between drift velocity and electric field. What is mobility? Describe the relation between mobility and velocity.

Drift velocity is the average velocity of charged particles, such as electrons or ions, in a material when subjected to an electric field. It is directly proportional to the electric field strength applied to the material.

The relationship between drift velocity (v_d) and electric field (E) can be described using the concept of mobility (μ). Mobility is a property of a charged particle in a material that characterizes its ability to move in response to an electric field. It is defined as the ratio of the drift velocity to the applied electric field:

μ = v_d / E

The mobility of a charged particle depends on various factors such as the nature of the material, temperature, and the concentration of charge carriers. It is typically expressed in units of square meters per volt-second (m^2/Vs).

The relationship between mobility and velocity can be understood by considering the motion of charged particles in a material. When an electric field is applied, the charged particles experience a force in the direction opposite to the field. This force causes them to accelerate, and as a result, they gain a certain drift velocity.

The mobility of a charged particle is a measure of how easily it can move through the material under the influence of an electric field. It takes into account factors such as the collisions between particles and impurities or lattice defects within the material. A higher mobility value indicates that the charged particle can move more easily, resulting in a higher drift velocity for a given electric field strength.

It is important to note that mobility and velocity are related but not the same. Velocity refers to the speed at which a particle is moving, while mobility specifically quantifies the ease of movement of a charged particle in response to an electric field. Mobility considers factors beyond just the velocity, such as the scattering mechanisms that affect the particle's motion.

In summary, the relationship between drift velocity and electric field is that the drift velocity is directly proportional to the electric field strength. Mobility represents the ratio of drift velocity to electric field and quantifies the ease of movement of charged particles. While velocity refers to the speed of a particle, mobility characterizes its ability to move in response to an electric field, considering various factors affecting its motion within a material.