If the magnetic field in a plane electromagnetic wave is given by B = 3 × 10-8 sin(1.6 × 103x + 48 × 1010t) j T, then what will be expression for electric field? (a) E = (9sin(1.6 × 103x + 48 × 1010t) k V/m) (b) E = (60sin(1.6 × 103x + 48 × 1010t) k V/m) (c) E = (3 × 10-8 sin(1.6 × 103x + 48 × 1010t) i V/m) (d) E = (3 × 10-8 sin(1.6 × 103x + 48 × 1010t) j V/m)

Answer: (a). v = 48×10¹⁰1.6×10³ = 3×10⁸ m/s; wave along -x. E₀ = cB₀ = 9 V/m; k× j = - i, so E along k. So the answer is (a) 9sin (1.6×10³x + 48×10¹⁰t) k V/m.

If the magnetic field in a plane electromagnetic wave is given by B =… | JEE Main 2020 (7 Jan, Shift 1)

Q56JEE Main 2020 · 7 JAN · SHIFT 1Medium

Nature of EM Waves & Wave Equation

If the magnetic field in a plane electromagnetic wave is given by

$\vec{B}$ = 3 $\times$ 10-8 sin(1.6 $\times$ 103x + 48 $\times$ 1010t) $\hat{j}$ T, then what will be expression for electric field?

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Answer: (a)

$v = \dfrac{48\times10^{10}}{1.6\times10^{3}} = 3\times10^{8}$ m/s; wave along $-x$ .
$E_0 = cB_0 = 9$ V/m; $\hat k\times\hat j = -\hat i$ , so $\vec E$ along $\hat k$ .
So the answer is (a) $9\sin(1.6\times10^{3}x + 48\times10^{10}t)\hat k$ V/m.

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Nature of EM Waves & Wave Equation question from JEE Main 2020 (7 Jan, Shift 1)

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