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What is Lorentz force ? Write an expression for it
Solution
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 | $10^{-12}$ |
