A proton of velocity (3 i +2 j ) m s^ -1 enters a field of magnetic induction (2 j +3 k ) tesla. The acceleration produced in the proton in m s^ -2 is (Specific charge of proton =0.96 × 10^8 C kg^ -1 )

Correct answer: B. 2.88 × 10^8(2 i -3 j +2 k ) Here, v =3 i +2 j ~m ~s^ -1 B =2 j +3 k ~TSpecific charge of proton = (e)/(m)= 0.96 × 10^8 C kg^ -1 Force on a proton in a uniform magnetic field is aligned & F =e( v × B ) & =e[(3 i +2 j ) ×(2 j +3 k )] & =e(6 k -9 j +6 i )=e(6 i -9 j +6 k ) N aligned Acceleration of the proton, aligned & a = F m = e(6 i -9 j +6 k ) m & =0.96 × 10^8(6 i -9 j +6 k ) m s^ -2 & =2.88 × 10^8(2 i -3 j +2 k ) m s^ -2 aligned

AIIMS 201926 May

Exam: AIIMS
Year: 2019
Date: 26 May
Subject: Physics
Chapter: Magnetic Effects of Current

AIIMS 2019 · 26 May · Physics · Magnetic Effects of Current

A proton of velocity (3 i +2 j ) m s^ -1 enters a field of magnetic...

A proton of velocity

(3 \hat{i}+2 \hat{j}) \mathrm{m} \mathrm{s}^{-1}

enters a field of magnetic induction

(2 \hat{j}+3 \hat{k})

tesla. The acceleration produced in the proton in

\mathrm{m} \mathrm{s}^{-2}

is (Specific charge of proton

=0.96 \times 10^8 \mathrm{C} \mathrm{kg}^{-1}

)

Options

A $2.8 \times 10^8(2 \hat{i}-3 \hat{j})$
B $2.88 \times 10^8(2 \hat{i}-3 \hat{j}+2 \hat{k})$
C $2.8 \times 10^8(2 \hat{i}+3 \hat{k})$
D $2.88 \times 10^8(\hat{i}-3 \hat{j}+2 \hat{k})$

Correct answer

B. $2.88 \times 10^8(2 \hat{i}-3 \hat{j}+2 \hat{k})$

Step-by-step solution

Here,

\vec{v}=3 \hat{i}+2 \hat{j} \mathrm{~m} \mathrm{~s}^{-1} \vec{B}=2 \hat{j}+3 \hat{k} \mathrm{~T}Specific charge

of proton =

\frac{e}{m}=

0.96 \times 10^8

\mathrm{C} \mathrm{kg}^{-1}

Force on a proton in a uniform magnetic field is

\begin{aligned} & \vec{F}=e(\vec{v} \times \vec{B}) \\ & =e[(3 \hat{i}+2 \hat{j}) \times(2 \hat{j}+3 \hat{k})] \\ & =e(6 \hat{k}-9 \hat{j}+6 \hat{i})=e(6 \hat{i}-9 \hat{j}+6 \hat{k}) \mathrm{N}\end{aligned}

Acceleration of the proton,

\begin{aligned} & \vec{a}=\frac{\vec{F}}{m}=\frac{e(6 \hat{i}-9 \hat{j}+6 \hat{k})}{m} \\ & =0.96 \times 10^8(6 \hat{i}-9 \hat{j}+6 \hat{k}) \mathrm{m} \mathrm{s}^{-2} \\ & =2.88 \times 10^8(2 \hat{i}-3 \hat{j}+2 \hat{k}) \mathrm{m} \mathrm{s}^{-2}\end{aligned}

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