Magnetic Effects Of Current Question 13
Question 13 - 2024 (31 Jan Shift 1)
An electron moves through a uniform magnetic field $\vec{B}=B_{0} \hat{i}+2 B_{0} \hat{j} T$. At a particular instant of time, the velocity of electron is $\vec{u}=3 \hat{i}+5 \hat{j} \mathrm{~m} / \mathrm{s}$. If the magnetic force acting on electron is $\vec{F}=5 \mathrm{ekN}$, where $\mathrm{e}$ is the charge of electron, then the value of $\mathrm{B}_{0}$ is T.
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Answer: (5)
Solution:
$\overrightarrow{\mathrm{F}}=\mathrm{q}(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}})$
$5 \mathrm{e} \hat{k}=\mathrm{e}(3 \hat{\mathrm{i}}+5 \hat{\mathrm{j}}) \times\left(\mathrm{B}{0} \hat{\mathrm{i}}+2 \mathrm{~B}{0} \hat{\mathrm{j}}\right)$
$5 \mathrm{e} \hat{k}=\mathrm{e}\left(6 \mathrm{~B}{0} \hat{\mathrm{k}}-5 \mathrm{~B}{0} \hat{\mathrm{k}}\right)$
$\Rightarrow \mathrm{B}_{0}=5 \mathrm{~T}$
