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 $\vec{F}=5 e \hat{k} N$, where $e$ is the charge of electron, then the value of $B_0$ is _________ $T$.
Answer (integer)
5
Solution
<p>$$\begin{aligned}
& \overrightarrow{\mathrm{F}}=\mathrm{q}(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}}) \\
& 5 \mathrm{e} \hat{\mathrm{k}}=\mathrm{e}(3 \hat{\mathrm{i}}+5 \hat{\mathrm{j}}) \times\left(\mathrm{B}_0 \hat{\mathrm{i}}+2 \mathrm{~B}_0 \hat{\mathrm{j}}\right) \\
& 5 \mathrm{e} \hat{\mathrm{k}}=\mathrm{e}\left(6 \mathrm{~B}_0 \hat{\mathrm{k}}-5 \mathrm{~B}_0 \hat{\mathrm{k}}\right) \\
& \Rightarrow \mathrm{B}_0=5 \mathrm{~T}
\end{aligned}$$</p>
About this question
Subject: Physics · Chapter: Magnetic Effects of Current · Topic: Biot-Savart Law
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