AIIMS2019Physics-Electromagnetism

AIIMS 2019 Physics Lorentz Force MCQ Question

Type: MCQ-numerical-Hard-Class 12

The expression of force is given by, 𝐹⃗ = 𝑄𝐸⃗ +𝑄(𝑉⃗ ×𝐡⃗ ) = (1.6Γ—10⁻¹⁹) [(10𝑖̂×10⁻⁢) + (1.6Γ—10⁻¹⁹) [(2𝑖̂) Γ— (𝑖̂ + 3𝑗̂ + 4π‘˜Μ‚)] Γ— 10⁻⁹ = (1.6Γ—10⁻¹⁹) [10𝑖̂ βˆ’ 8𝑗̂ + 6π‘˜Μ‚] Γ— 10⁻⁢ N Calculate the acceleration as follows, π‘Žβƒ— = (1.6Γ—10⁻¹⁹) [10𝑖̂ βˆ’ 8𝑗̂ + 6π‘˜Μ‚] Γ— 10⁻⁢ N / 1.6Γ—10⁻²⁷ = 1400 m/sΒ²

Correct Answer

Option A

Detailed Explanation

Option A is correct because the calculated acceleration, aβƒ—=(1.6Γ—10βˆ’19)[10i^βˆ’8j^+6k^]Γ—10βˆ’6 N1.6Γ—10βˆ’27 kg\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 1400 m/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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