An electron moves through a uniform magnetic field vec{B}=B_0 hat{i}+2 B_0 hat{j} T . At a particula

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4.Moving Charges and Magnetism

hard

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 $\overrightarrow{\mathrm{u}}=3 \hat{i}+5 \hat{j} \mathrm{~m} / \mathrm{s}$. If the magnetic force acting on electron is $\vec{F}=5 e\hat kN$, where $e$ is the charge of electron, then the value of $\mathrm{B}_0$ is ____$\mathrm{T}$.

A

$5$

B

$6$

C

$7$

D

$8$

(JEE MAIN-2024)

Solution

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

$5 e \hat{k}=e(3 \hat{i}+5 \hat{j}) \times\left(B_0 \hat{i}+2 B_0 \hat{j}\right)$

$5 e \hat{k}=e\left(6 B_0 \hat{k}-5 B_0 \hat{k}\right)$

$\Rightarrow B_0=5 T$

Standard 12

Physics

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