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Magnetic Field — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsMagnetic Field5 Marks
Question
When a proton is released from rest in a room, it starts with an initial acceleration $a_0$ towards west. When it is projected towards north with a speed $v_0$, it moves with an initial acceleration $3a_0$ towards west. Find the electric field and the maximum possible magnetic field in the room.
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Answer

$\text{q}_\text{p}=\text{e},\ \text{mp}=\text{m},\ \text{F}=\text{q}_\text{p}\times\text{E}$
$\text{ma}_0=\text{eE}$
$\text{E}=\frac{\text{ma}_0}{\text{e}}$ towards west

The acceleration changes from $a_0$ to $3a_0$
Hence net acceleration produced by magnetic field $\overrightarrow{\text{B}}$ is $2a_0.$
Force due to magnetic field
$\overrightarrow{\text{F}}_\text{B}=\text{m}\times2\text{a}_0=\text{e}\times\text{V}_0\times\text{B}$
$\Rightarrow\text{B}=\frac{2\text{ma}_0}{\text{eV}_0}$ downwards

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