Electromagnetic Waves

JEE Main level, single correct, medium

20 of 165

Question 20 of 165

Two plane polarized light waves combine at a certain point whose electric field components are
E1=E0sin⁡ωtE2=E0sin⁡(ωt+π3)\begin{aligned} & \mathrm{E}_1=\mathrm{E}_0 \sin \omega \mathrm{t} \\ & \mathrm{E}_2=\mathrm{E}_0 \sin \left(\omega \mathrm{t}+\frac{\pi}{3}\right)\end{aligned}
Find the amplitude of the resultant wave.

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Answer: (C) 1.7E01.7 \mathrm{E}_0

E=(E0)2+(E0)2+2(E0)(E0)cos⁡π3\mathrm{E}=\sqrt{\left(\mathrm{E}_0\right)^2+\left(\mathrm{E}_0\right)^2+2\left(\mathrm{E}_0\right)\left(\mathrm{E}_0\right) \cos \frac{\pi}{3}}
E=2E02+E02=3E0=1.73E0\mathrm{E}=\sqrt{2 \mathrm{E}_0^2+\mathrm{E}_0^2}=\sqrt{3} \mathrm{E}_0=1.73 \mathrm{E}_0

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