AIIMS2019Physics-Electromagnetism

AIIMS 2019 Physics Lorentz Force MCQ Question

Type: MCQ-numerical-Hard-Class 12

A proton is projected with velocity V=2i^\vec{\text{V}} = 2\hat{\text{i}} in a region where magnetic field B=(i^+3j^+4k^)μT\vec{\text{B}} = \left(\hat{\text{i}} + 3\hat{\text{j}} + 4\hat{\text{k}}\right)\mu\text{T} and electric field E=10i^ μV/m\vec{\text{E}} = 10\hat{\text{i}}\ \mu\text{V/m}. Then find out the net acceleration of proton:

A

1400 m/s21400\text{ m/s}^2

B

700 m/s2700\text{ m/s}^2

C

1000 m/s21000\text{ m/s}^2

D

800 m/s2800\text{ m/s}^2

Correct Answer

Option A

Detailed Explanation

Option A is correct because the calculated acceleration, a=(1.6×1019)[10i^8j^+6k^]×106N1.6×1027kg\vec{a} = \frac{(1.6 \times 10^{-19}) [10 \hat{i} - 8 \hat{j} + 6 \hat{k}] \times 10^{-6} \, \text{N}}{1.6 \times 10^{-27} \, \text{kg}}, simplifies to 1400m/s21400 \, \text{m/s}^2, demonstrating the relationship between force, mass, and acceleration as described by Newton's second law, F=maF = ma. Other options are not applicable as they do not provide any alternative values or explanations relevant to the problem at hand. This exercise illustrates the importance of vector operations in calculating forces and subsequent accelerations in a magnetic field.

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