Question

The correct expression for Lorentz force is
$\begin{align}
  & \text{A}\text{. q}\left[ \overrightarrow{E}+\left( \overrightarrow{B}\times \overrightarrow{V} \right) \right] \\
 & \text{B}\text{. q}\left[ \overrightarrow{E}+\left( \overrightarrow{V}\times \overrightarrow{B} \right) \right] \\
 & \text{C}\text{. q}\left( \overrightarrow{V}\times \overrightarrow{B} \right) \\
 & \text{D}\text{. q}\overrightarrow{E} \\
\end{align}$

Answer 1

Hint: A charged particle moving through a magnetic field experiences a force, which is at the right angle to both the direction in which the particle is moving and the direction of the applied magnetic field. This force is called the Lorentz force. Lorentz force develops an equation that mathematically relates the force on the particle to the velocity and charge of the particle and the strength of the applied magnetic field.

Complete step-by-step answer:
Lorentz force is described as the combination of the magnetic force and the electric force on a point charge when placed in an electromagnetic field. The Lorentz force is used in the electromagnetism, combination of electricity and magnetism, and is also known as the electromagnetic force.

Electric force on a charged particle is given by,
${{\overrightarrow{F}}_{E}}=q\overrightarrow{E}$
Where,
$q$ is the electric charge on the particle
$E$ is the external electric field
Magnetic force on a charged particle is given by,
$\begin{align}
  & {{\overrightarrow{F}}_{B}}=q\left( \overrightarrow{V}\times \overrightarrow{B} \right) \\
 & {{\overrightarrow{F}}_{B}}=qVB\sin \theta \\
\end{align}$
$q$ is the electric charge on the particle
$V$ is the velocity of the particle
$B$ is the external the magnetic field
$\theta $ is the angle between velocity and the magnetic field
Expression for the Lorentz force experienced by a charged particle is given as:
$\begin{align}
  & \overrightarrow{F}={{\overrightarrow{F}}_{E}}+{{\overrightarrow{F}}_{B}} \\
 & \overrightarrow{F}=q\overrightarrow{E}+q\left( \overrightarrow{V}\times \overrightarrow{B} \right) \\
 & \overrightarrow{F}=q\left[ \overrightarrow{E}+\left( \overrightarrow{V}\times \overrightarrow{B} \right) \right] \\
\end{align}$
Where,
$F$ is the force acting on the particle
$q$ is the electric charge of the particle
$V$ is the velocity of the particle
$E$ is the external electric field
$B$ is the external the magnetic field
Lorentz force helps to explain the mathematical equations along with the physical importance of the forces, electric force and magnetic force, acting on the charged particles that are traveling through the space containing the electric field as well as the magnetic field. This is the importance of the Lorentz force.
The applications of the Lorentz Force are:
i. Cyclotrons and other particle accelerators use the phenomenon of Lorentz force.
ii. A bubble chamber uses Lorentz force to generate the graph for getting the trajectories of the charged particles.
iii. Cathode ray tube televisions use the concept of Lorentz force to deviate the path of the electrons in a straight line in order to make them land on the specific spots on the screen.
The expression for Lorentz force is $\overrightarrow{F}=q\left[ \overrightarrow{E}+\left( \overrightarrow{V}\times \overrightarrow{B} \right) \right]$

So, the correct answer is “Option B”.

Note: The Lorentz force is the force experienced by an electrically charged particle that moves through a magnetic plus an electric field. The Lorentz force is composed of two vector components, one proportional to the magnetic field and the other proportional to the electric field. These components must be added vectorially, in vector form, to obtain the total force.