Physics

Physics

Problem

A plane wave is represented by E(x,t)=60 sin⁡(6πx−1.8×1010πt)  V m−1.E(x,t)=60\,\sin\bigl(6\pi x-1.8\times10^{10}\pi t\bigr)\;\text{V\,m}^{-1}. At t=2.5×10−10 st = 2.5\times10^{-10}\,\text{s}, the electric field reaches its maximum positive value at several positions along the xx-axis. What is the smallest positive value of xx (in metres) where this occurs? a) 0.500.50 b) 0.170.17 c) 0.0830.083 d) 0.2650.265
Intuitive explanation

A plane wave's electric field reaches its maximum when the argument of the sine function equals π/2\pi/2. You need to find where the phase 6πx−1.8×1010πt6\pi x - 1.8 \times 10^{10}\pi t equals π/2\pi/2 at the given time, then solve for the smallest positive xx. This combines understanding wave phase with algebraic manipulation—substitute the time, set the phase condition, and isolate xx.

Intuitive explanation

A plane wave's electric field reaches its maximum when the argument of the sine function equals π/2\pi/2. You need to find where the phase 6πx−1.8×1010πt6\pi x - 1.8 \times 10^{10}\pi t equals π/2\pi/2 at the given time, then solve for the smallest positive xx. This combines understanding wave phase with algebraic manipulation—substitute the time, set the phase condition, and isolate xx.

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