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.

JEE Main · 2024 · 31 Jan 2024 · Shift 1 · Magnetic Effects of Current

An electron moves through a uniform magnetic field

B = B_{0} \hat{i} + 2 B_{0} \hat{j}

T. At a particular instant of time, the velocity of electron is

u = 3 \hat{i} + 5 \hat{j}

m/s. If the magnetic force acting on electron is

F = 5 e \hat{k}

N, where e is the charge of electron, then the value of

B_{0}

is ______ T.

Answer: 5

Solution

Using

F = q (v \times B)

for the electron:

v \times B = (3 \hat{i} + 5 \hat{j}) \times (B_{0} \hat{i} + 2 B_{0} \hat{j}) = 3 B_{0} \cdot 2 (\hat{i} \times \hat{j}) + 5 B_{0} (\hat{j} \times \hat{i}) = 6 B_{0} \hat{k} - 5 B_{0} \hat{k} = B_{0} \hat{k}

Matching magnitudes with the given force

F = 5 e \hat{k}

e \cdot B_{0} = 5 e ⟹ B_{0} = 5 T

JEE Main · 2024 · 31 Jan 2024 · Shift 1 · Integer answer

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