Question

In the case of the Hall effect for a strip having charge $Q$and area of cross-section $A$, the Lorentz force is
A.Directly proportional to $Q$
B.Inversely proportional to $Q$
C.Inversely proportional to $A$
D.Directly proportional to $A$

Answer 1

Hint: Hall effect is nothing but an extension of the Lorentz force, which indicates force exerted by an electron moving in a magnetic field. If the magnetic field is perpendicular to the direction of motion of the electron, the electron experiences a force called the Lorentz force.




Complete answer:

A Hall effect is a process where a transverse electric field is produced in a solid material carrying current and is placed in a uniform magnetic field that is at the right angle to the current. This effect indicates a potential difference develops between the two sides of the conductor.
When a magnetic field is applied perpendicular to the flow of current, the field develops resistance in the current This is a manifestation of Lorentz force, which attracts the negatively charged electrons in the current in the direction governed by Fleming’s left-hand thumb rule. This results in a weak but measurable voltage perpendicular to both the magnetic field and current flow. This is mainly known as the Halt effect.
Consider a charged particle $Q$ is moving through a uniform magnetic field, then the magnetic force or Lorentz force $\vec{F}$ experienced by the charged particle is perpendicular to the direction of velocity $\vec{v}$ and orientation of the magnetic field $\vec{B}$.
$\therefore \vec{F}=Q(\vec{B}\times \vec{v})$
Or,$\vec{F}$ $\alpha $ $Q$
That is, the Lorentz force is directly proportional to the charge of the particle $Q$.
Thus, option (A) is correct.



Note: Hall effect has many practical applications such as the halt effect sensor being used as a Current sensor, in magnetometers, as an automotive fuel level indicator, in phase angle measurement, etc. This effect is useful to examine whether the material is an insulator or semiconductor.