A charge particle is moving in a uniform magnetic field (2 i +3 j ) T . If it has an acceleration of (α i -4 j ) m / s^2 , then the value of α will be :

Correct answer: B. 6 Given that uniform magnetic field, B =(2 i +3 j ) T Acceleration a =(α i -4 j ) m / s^2 We know that F=q( v × B ) m a =q( v × B ) Here, a B , so, a · B =0 (α i -4 j )(2 i +3 j )=0 2 α-12=0 α=6

BITSAT 2023Paper 1

Exam: BITSAT
Year: 2023
Paper: Paper 1
Subject: Physics
Chapter: Magnetic Effects of Current

BITSAT 2023 · Paper 1 · Physics · Magnetic Effects of Current

A charge particle is moving in a uniform magnetic field (2 i +3 j )...

A charge particle is moving in a uniform magnetic field

(2 \hat{i}+3 \hat{j}) \mathrm{T}

. If it has an acceleration of

(\alpha \hat{i}-4 \hat{j}) \mathrm{m} / \mathrm{s}^2

, then the value of

\alpha

will be :

Options

Correct answer

B. 6

Step-by-step solution

Given that uniform magnetic field,

\vec{B}=(2 \hat{i}+3 \hat{j}) T

Acceleration

\vec{a}=(\alpha \hat{i}-4 \hat{j}) \mathrm{m} / \mathrm{s}^2

We know that

F=q(\vec{v} \times \vec{B}) \Rightarrow m \vec{a}=q(\vec{v} \times \vec{B})

Here,

\vec{a} \perp \vec{B}

, so,

\vec{a} \cdot \vec{B}=0

(\alpha \hat{i}-4 \hat{j})(2 \hat{i}+3 \hat{j})=0 \Rightarrow 2 \alpha-12=0 \Rightarrow \alpha=6

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