Magnetic Effects & Magnetism

JEE Main level, single correct, medium

150 of 276

Question 150 of 276

An electron is constrained to move along the yy-axis with a speed of 0.1c0.1c (c is the speed of light) in the presence of electromagnetic wave, whose electric field is E⃗=30j^sin⁡(1.5×107t−5×10−2x)Vm−1.\vec{E}=30\hat{j}\sin \left(1.5\times {10}^{7}t-5\times {10}^{-2}x\right)V{m}^{-1}. where tt in in seconds and xx is im meters.The maximum magnetic force experienced by the electron will be: (given c=3×108ms−1c=3\times {10}^{8}m{s}^{-1} and electron charge =1.6×10−19Coloumbs=1.6\times {10}^{-19}Coloumbs

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Answer: (C) 4.8×10−19N4.8\times {10}^{-19}N

In electromagnetic wave is E0B0=C\dfrac{{E}_{0}}{{B}_{0}}=C
so maximum value of magnetic field is
B0=E0C{B}_{0}=\dfrac{{E}_{0}}{C}
Fmax=qVBmax⋅sin⁡90∘{F}_{max}=qV{B}_{max}\cdot \sin 90^{\circ}
=qV0E0CN=\dfrac{q{V}_{0}{E}_{0}}{C}N
1.6×10−19×0.1×3×108×303×108=4.8×10−19N\dfrac{1.6\times {10}^{-19}\times 0.1\times 3\times {10}^{8}\times 30}{3\times {10}^{8}}=4.8\times {10}^{-19}N

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