What is Lorentz force ? Write an expression for it
What is Lorentz force ? Write an expression for it
The total force experienced by a charged particle moving in a region where both electric and magnetic fields are present is called Lorentz force.
A charge $q$ in an electric field $\overrightarrow{\mathrm{E}}$ experiences the electric force,
$\overrightarrow{\mathrm{F}}_{\mathrm{e}}=q \overrightarrow{\mathrm{E}}$
The magnetic force experienced by the charge $q$ moving with velocity $\vec{V}$ in the magnetic field $\overrightarrow{\mathrm{B}}$ is given by,
$\overrightarrow{\mathrm{F}}_{\mathrm{m}}=q(\vec{v} \times \overrightarrow{\mathrm{B}})$
So, total force experienced by the charge $q$ due to both,
$\overrightarrow{\mathrm{F}}=\overrightarrow{\mathrm{F}}_{\mathrm{e}}+\overrightarrow{\mathrm{F}}_{\mathrm{m}}$ $=q \overrightarrow{\mathrm{E}}+q(\vec{v} \times \overrightarrow{\mathrm{B}})$ $\therefore \overrightarrow{\mathrm{F}} =q[\overrightarrow{\mathrm{E}}+(\vec{v} \times \overrightarrow{\mathrm{B}})] \text { This force is known as Lorentz force. }$
Order of magnitudes of magnetic fields in a variety of physical situations.
| Physical situation | Magnitude of $B$(in tesla) |
| surface of a neutron star | $10^{8}$ |
| large field in a laboratory | $1$ |
| near a small bar magnet | $10^{-2}$ |
| o the earth's surface | $10^{-5}$ |
| human nerve fiber | $10^{-10}$ |
| intersteller space | $10^{-12}$ |
Similar Questions
An electron moves with a speed of $2 \times 10^5\, m/s$ along the $+ x$ direction in a magnetic field $\vec B = \left( {\hat i - 4\hat j - 3\hat k} \right)\,tesla$. The magnitude of the force (in newton) experienced by the electron is (the charge on electron $= 1.6 \times 10^{-19}\, C$)
An electron moves with a speed of $2 \times 10^5\, m/s$ along the $+ x$ direction in a magnetic field $\vec B = \left( {\hat i - 4\hat j - 3\hat k} \right)\,tesla$. The magnitude of the force (in newton) experienced by the electron is (the charge on electron $= 1.6 \times 10^{-19}\, C$)
A charge particle of $2\,\mu\,C$ accelerated by a potential difference of $100\,V$ enters a region of uniform magnetic field of magnitude $4\,m\,T$ at right angle to the direction of field. The charge particle completes semicircle of radius $3\,cm$ inside magnetic field. The mass of the charge particle is $........\times 10^{-18}\,kg$.
A charge particle of $2\,\mu\,C$ accelerated by a potential difference of $100\,V$ enters a region of uniform magnetic field of magnitude $4\,m\,T$ at right angle to the direction of field. The charge particle completes semicircle of radius $3\,cm$ inside magnetic field. The mass of the charge particle is $........\times 10^{-18}\,kg$.
- [JEE MAIN 2023]
A block of mass $m$ $\&$ charge $q$ is released on a long smooth inclined plane magnetic field $B$ is constant, uniform, horizontal and parallel to surface as shown. Find the time from start when block loses contact with the surface.
A block of mass $m$ $\&$ charge $q$ is released on a long smooth inclined plane magnetic field $B$ is constant, uniform, horizontal and parallel to surface as shown. Find the time from start when block loses contact with the surface.
A particle is projected with a velocity ( $10\ m/s$ ) along $y-$ axis from point $(2, 3)$ . Magnetic field of $\left( {3\hat i + 4\hat j} \right)$ Tesla exist uniformly in the space. Its speed when particle passes through $y-$ axis for the third time is : (neglect gravity)
A particle is projected with a velocity ( $10\ m/s$ ) along $y-$ axis from point $(2, 3)$ . Magnetic field of $\left( {3\hat i + 4\hat j} \right)$ Tesla exist uniformly in the space. Its speed when particle passes through $y-$ axis for the third time is : (neglect gravity)
Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields $\vec{E}=E_0 \hat{j}$ and $\vec{B}=B_0 \hat{j}$. At time $t=0$, this charge has velocity $\nabla$ in the $x$-y plane, making an angle $\theta$ with $x$-axis. Which of the following option$(s)$ is(are) correct for time $t>0$ ?
$(A)$ If $\theta=0^{\circ}$, the charge moves in a circular path in the $x-z$ plane.
$(B)$ If $\theta=0^{\circ}$, the charge undergoes helical motion with constant pitch along the $y$-axis.
$(C)$ If $\theta=10^{\circ}$, the charge undergoes helical motion with its pitch increasing with time, along the $y$-axis.
$(D)$ If $\theta=90^{\circ}$, the charge undergoes linear but accelerated motion along the $y$-axis.
Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields $\vec{E}=E_0 \hat{j}$ and $\vec{B}=B_0 \hat{j}$. At time $t=0$, this charge has velocity $\nabla$ in the $x$-y plane, making an angle $\theta$ with $x$-axis. Which of the following option$(s)$ is(are) correct for time $t>0$ ?
$(A)$ If $\theta=0^{\circ}$, the charge moves in a circular path in the $x-z$ plane.
$(B)$ If $\theta=0^{\circ}$, the charge undergoes helical motion with constant pitch along the $y$-axis.
$(C)$ If $\theta=10^{\circ}$, the charge undergoes helical motion with its pitch increasing with time, along the $y$-axis.
$(D)$ If $\theta=90^{\circ}$, the charge undergoes linear but accelerated motion along the $y$-axis.
- [IIT 2012]