A charge moves with velocity ' $\mathrm{V}$ ' through electric field (E) as well as magnetic field (B). then…

A charge moves with velocity ' $\mathrm{V}$ ' through electric field (E) as well as magnetic field (B). then the force acting on it is
  1. $\mathrm{q}(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{V}})$
  2. $q(\overrightarrow{\mathrm{V}} \times \overrightarrow{\mathrm{B}})$
  3. $q \overrightarrow{\mathrm{E}}+\mathrm{q}(\overrightarrow{\mathrm{V}} \times \overrightarrow{\mathrm{B}})$
  4. $\mathrm{q}(\overrightarrow{\mathrm{E}} \times \overrightarrow{\mathrm{V}})$

Solution

Force due to electric field $\overrightarrow{\mathrm{F}}_{\mathrm{e}}=\mathrm{q} \overrightarrow{\mathrm{E}}$ Force due to magnetic field $\overrightarrow{\mathrm{F}}_{\mathrm{m}}=\mathrm{q}(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}})$ $\therefore$ Total force $\overrightarrow{\mathrm{F}}=\mathrm{q} \overrightarrow{\mathrm{E}}+\mathrm{q}(\overrightarrow{\mathrm{V}} \times \overrightarrow{\mathrm{B}})$ *

Asked in: MHT CET 2021 (21 Sep Shift 1)

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