First slide

Introduction-Electromagnetic waves

Question

The magnetic field in a plane electromagnetic wave is given by $B y = 2 \times 10^{- 7} \sin (0.1 \times 10^{3} x + 1.1 \times 10^{11} t) T$ . Write an expression for the electric field

Easy

A

$6 \sin (0.1 \times 10^{3} x + 1.1 \times 10^{11} t) V / m$
B

$60 \sin (0.1 \times 10^{3} x + 1.1 \times 10^{11} t) V / m$
C

$6 \times 10^{3} \sin (0.1 x + 1.1 t) V / m$
D

$0.6 \sin (0.1 \times 10^{3} x - 1.1 \times 10^{11} t) V / m$

Solution

Step no 1:
$E_{o} = C B_{o} = 3 \times 10^{8} \times 2 \times 10^{- 7} = 60 V / m$
Step no 2:
In electromagnetic wave, the electric field is varying sinusoidally with x and ‘t’ perpendicular to the direction of magnetic field as well as the direction of electro magnetic wave. So electric field is varying along Z- direction
Step 3: Thus $E_{z} = E_{o} \sin (\frac{2 π}{λ} x + \frac{2 π}{λ} t)$
$E_{z} = 60 \sin (0.1 \times 10^{3} x + 1.1 \times 10^{11} t) V / m$

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