A proton of velocity 3i^+2j^ ms-1 enters a field of magnetic induction 2j^+3k^ tesla. The acceleration produced in the proton in ms-2 is (Specific charge of proton =0.96×108 C kg-1)

Here, v→=3i^+2j^ ms-1 and B→=2j^+3k^ T Specific charge of proton =em=0.96×108 C kg-1 Force on a proton in a uniform magnetic field is F→=ev→×B→=e3i^+2j^×2j^+3k^ =e6k^-9j^+6i^=e6i^-9j^+6k^N Acceleration of the proton, a→=F→m=e6i^-9j^+6k^m=0.96×1086i^-9j^+6k^ ms-2 =2.88×1082i^-3j^+2k^ ms-2

A proton of velocity 3i^+2j^ ms-1 enters a field of magnetic induction 2j^+3k^ tesla. The acceleration produced in the proton in ms-2 is (Specific charge of proton =0.96×108 C kg-1)

Here, v→=3i^+2j^ ms-1 and B→=2j^+3k^ T Specific charge of proton =em=0.96×108 C kg-1 Force on a proton in a uniform magnetic field is F→=ev→×B→=e3i^+2j^×2j^+3k^ =e6k^-9j^+6i^=e6i^-9j^+6k^N Acceleration of the proton, a→=F→m=e6i^-9j^+6k^m=0.96×1086i^-9j^+6k^ ms-2 =2.88×1082i^-3j^+2k^ ms-2

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

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$2.8 \times 10^{8} (2 \hat{i} - 3 \hat{j})$

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

$2.8 \times 10^{8} (2 \hat{i} + 3 \hat{k})$

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

answer is B.

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Detailed Solution

Here, $\vec{v} = 3 \hat{i} + 2 \hat{j} m s^{- 1}$ and $\vec{B} = 2 \hat{j} + 3 \hat{k} T$

Specific charge of proton $= \frac{e}{m} = 0.96 \times 10^{8} C k g^{- 1}$

Force on a proton in a uniform magnetic field is

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

Acceleration of the proton,

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