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 $\vec{u}=3 \hat{i}+5 \hat{j} m / s$. If the magnetic force acting on electron is $\vec{F}=5 ekN$, where $e$ is the charge of electron, then the value of $B _0$ is T.
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Answer: (5)
Solution:
$\overrightarrow{F}=q(\overrightarrow{v} \times \overrightarrow{B})$
$5 e \hat{k}=e(3 \hat{i}+5 \hat{j}) \times\left(B _0 \hat{i}+2 B _0 \hat{j}\right)$
$5 e \hat{k}=e\left(6 B _0 \hat{k}-5 B _0 \hat{k}\right)$
$\Rightarrow B _0=5 T$
