
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
163.2k+ views
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.
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.
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