### 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.

## Show Answer

#### Answer: (5)

#### Solution:

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

$5 e \hat{k}=e(3 \hat{i}+5 \hat{j}) \times\left(B _0 \hat{i}+2 B _0 \hat{j}\right)$

$5 e \hat{k}=e\left(6 B _0 \hat{k}-5 B _0 \hat{k}\right)$

$\Rightarrow B _0=5 T$