
Lorentz force can be calculated by using the formula
A. \[\vec F = q\left[ {\vec E + \vec v \times \vec B} \right]\]
B. \[\vec F = q\left[ {\vec E - \vec v \times \vec B} \right]\]
C. \[\vec F = q\left[ {\vec E dot \vec v \times \vec B} \right]\]
D. \[\vec F = q\left[ {\vec E + \vec B + \vec v} \right]\]
Answer
162.9k+ views
Hint: In the given question, we need to find the formula of Lorentz force. For this, we need to use the concept that the Lorentz Force is defined as the force on a charged particle due to electric as well as magnetic fields to get the desired result.
Complete answer:
We know that a charged particle moving at speed \[v\] through an electric field \[E\]and a magnetic field \[B\] experiences the Lorentz force.
Mathematically, it is defined as
\[\vec F = {\vec F_e} + {\vec F_m}\]
Here, \[{\vec F_e}\]is the force vector due to electric field and \[{\vec F_m}\]is the force vector due to magnetic field
But \[{\vec F_e} = q\vec E\] and \[{\vec F_m} = q(\vec v \times \vec B)\]
Here, \[q\] is the charge.
Thus, we get
\[\vec F = q\vec E + q(\vec v \times \vec B)\]
By simplifying, we get
\[\vec F = q\left[ {\vec E + \vec v \times \vec B} \right]\]
Thus, we can say that Lorentx force can be calculated by using the formula \[\vec F = q\left[ {\vec E + \vec v \times \vec B} \right]\].
Therefore, the correct option is (A).
Additional Information : The electromagnetic field-induced magnetic and electric forces acting on a point charge are referred to as the Lorentz force. It is also referred to as the electromagnetic force and it is used in electromagnetism. Hendrik Lorentz developed the present Lorentz force formula in\[1895\]. Also, the physical significance of force applied on charged particles as they travel through space with an electric and magnetic field is explained by Lorentz's force, which also describes the mathematical equations behind them.
Note: Many students make mistakes in writing the formula of the Lorentz force. This is the only way through which we can solve the example in the simplest way. Also, it is essential to analyse the concept of Lorentz force carefully to get the desired result regarding proton and electron.
Complete answer:
We know that a charged particle moving at speed \[v\] through an electric field \[E\]and a magnetic field \[B\] experiences the Lorentz force.
Mathematically, it is defined as
\[\vec F = {\vec F_e} + {\vec F_m}\]
Here, \[{\vec F_e}\]is the force vector due to electric field and \[{\vec F_m}\]is the force vector due to magnetic field
But \[{\vec F_e} = q\vec E\] and \[{\vec F_m} = q(\vec v \times \vec B)\]
Here, \[q\] is the charge.
Thus, we get
\[\vec F = q\vec E + q(\vec v \times \vec B)\]
By simplifying, we get
\[\vec F = q\left[ {\vec E + \vec v \times \vec B} \right]\]
Thus, we can say that Lorentx force can be calculated by using the formula \[\vec F = q\left[ {\vec E + \vec v \times \vec B} \right]\].
Therefore, the correct option is (A).
Additional Information : The electromagnetic field-induced magnetic and electric forces acting on a point charge are referred to as the Lorentz force. It is also referred to as the electromagnetic force and it is used in electromagnetism. Hendrik Lorentz developed the present Lorentz force formula in\[1895\]. Also, the physical significance of force applied on charged particles as they travel through space with an electric and magnetic field is explained by Lorentz's force, which also describes the mathematical equations behind them.
Note: Many students make mistakes in writing the formula of the Lorentz force. This is the only way through which we can solve the example in the simplest way. Also, it is essential to analyse the concept of Lorentz force carefully to get the desired result regarding proton and electron.
Recently Updated Pages
JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Chemical Properties of Hydrogen - Important Concepts for JEE Exam Preparation

JEE Energetics Important Concepts and Tips for Exam Preparation

JEE Isolation, Preparation and Properties of Non-metals Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Degree of Dissociation and Its Formula With Solved Example for JEE

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

Charging and Discharging of Capacitor

Wheatstone Bridge for JEE Main Physics 2025

Formula for number of images formed by two plane mirrors class 12 physics JEE_Main

In which of the following forms the energy is stored class 12 physics JEE_Main
