An electron moves through a uniform magnetic field . At a particular instant of time, the velocity of electron is m/s. If the magnetic force acting on electron is , where e is the charge of electron, then the value of is

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Solution

Q.
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 $\vec{F} = 5 e \hat{k}$ $N$ , where e is the charge of electron, then the value of $B_{0}$ is ____ T. [2024]

Ans.
(5) $\vec{F} = q (\vec{v} \times \vec{B})$

$5 e \hat{k} = e (3 \hat{i} + 5 \hat{j}) \times (B_{0} \hat{i} + 2 B_{0} \hat{j})$

$5 e \hat{k} = e (6 B_{0} \hat{k} - 5 B_{0} \hat{k}) \Rightarrow B_{0} = 5 T$

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