Question

The electric field of an electromagnetic wave in free space is given by $stack bold E bold space with rightwards arrow on top space equals space 10 space cos space left parenthesis 10 to the power of 7 space straight t space space plus kx right parenthesis bold j with hat on top space straight V divided by straight m$ , where t and x are in seconds and meters respectively. It can be inferred that

1) the wavelength λ is 188.4 m.
2)The wave number k is 0.33 rad/m.
3)The wave amplitude is 10 V /m.
4)The wave is propagating along +x direction

(3) and (4)

(1) and (2)

(2) and (3)

(1) and (3)

Solution

(1) and (3)

The electric field of electromagnetic wave
$stack bold E bold space with rightwards arrow on top space equals space 10 space cos space left parenthesis 10 to the power of 7 space straight t space space plus kx right parenthesis bold j with hat on top space straight V divided by straight m amplitude space equals space 10 space straight V because space straight c space equals space straight omega over straight k therefore space 3 space straight x space 10 to the power of 8 space equals space 10 to the power of 7 over straight k straight k space equals space 1 over 30 or space fraction numerator 2 straight pi over denominator straight lambda end fraction space equals space 1 over 30 or space straight lambda space equals space 188.4 space straight m$

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Electric Charges And Fields

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

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