
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
134.1k+ 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 Main 2025 Session 2 Form Correction (Closed) – What Can Be Edited

Sign up for JEE Main 2025 Live Classes - Vedantu

JEE Main Books 2023-24: Best JEE Main Books for Physics, Chemistry and Maths

JEE Main 2023 April 13 Shift 1 Question Paper with Answer Key

JEE Main 2023 April 11 Shift 2 Question Paper with Answer Key

JEE Main 2023 April 10 Shift 2 Question Paper with Answer Key

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

JEE Main 2025: Conversion of Galvanometer Into Ammeter And Voltmeter in Physics

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Wheatstone Bridge for JEE Main Physics 2025

Electric field due to uniformly charged sphere class 12 physics JEE_Main

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

Diffraction of Light - Young’s Single Slit Experiment

Dual Nature of Radiation and Matter Class 12 Notes: CBSE Physics Chapter 11

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

JEE Advanced 2024 Syllabus Weightage

JEE Main Chemistry Question Paper with Answer Keys and Solutions
