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JEE MAINS 2024
31.01.24 S1
Question
An electron moves through a uniform magnetic field B ⃗=B_0 i ˆ+2B_0 j ˆT. At a particular instant of time, the velocity of electron is u ⃗=3i ˆ+5j ˆm/s. If the magnetic force acting on electron is F ⃗=5ekN, where e is the charge of electron, then the value of B_0 is T.
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Solution
$\begin{array}{ll}\text { Sol. } & \vec{F}=q(\vec{v} \times \vec{B}) \\ & 5 e \hat{k}=e(3 \hat{i}+5 \hat{j}) \times\left(B_0 \hat{i}+2 B_0 \hat{j}\right) \\ & 5 e \hat{k}=e\left(6 B_0 \hat{k}-5 B_0 \hat{k}\right) \\ & \Rightarrow B_0=5 T\end{array}$
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