GATE EC 2005 Electromagnetics Solution Q 1

GATE EC 2005 Electromagnetics Solution Q 1

The magnetic field intensity vector of a plane wave is given by

\overline H(x,t)=10\sin\;(50000t+0.004x+30){\overline a}_y,

where {\widehat a}_ydenotes the unit vector in y direction. The wave is propagating with a phase velocity

(a) 5\times10^4m/s

(b) 3\times10^8m/s

(c) 1.25\times10^7m/s

(d) 3\times10^6m/s

Ans : (c)

Explanation

Comparing with the standard wave equation, we have,

\omega=50,000\;\;\;\;and\;\;\;\;\;\beta=0.004 \therefore v_p=\frac\omega\beta=\frac{5\times10^4}{4\times10^{-3}}=1.25\times10^7m/s

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