Physics Electromagnetic Waves

Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by E = $20 c o s (2 * 1 0^{10} t - 200 x) V / m .$ The dielectric constant of the medium is equal to:

(Take $μ_{r} = 1)$

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Physics Electromagnetic Waves Electromagnetic Waves

Contributor-Level 10

Comparing E = 20 cos (2 * 10¹⁰ t – 200x) V/m to

$E = E_{0} c o s (ω t - k x) v / m$

$ω = 2 * 1 0^{10}, K = 200$

Speed = $\frac{2 * 1 0^{10}}{200} = 1 0^{8} m / s$

R.I. $= \frac{C}{s p e e d} = \frac{3 * 1 0^{8}}{1 0^{8}} = 3$

$N o w R . I . = \sqrt[]{ε_{r} μ_{r}}$

$3 = \sqrt[]{ε_{r} * 1}$

$ε_{r} = 9$

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The magnetic field vector of an electromagnetic wave is given by B = B₀ = $\frac{\hat{i} + \hat{j}}{\sqrt[]{2}} c o s (k z - ω t);$ where $\hat{i}, \hat{j}$ represents unit vector along x and y-axis respectively. At t = 0 s, two electric charges q1 of 4π coulomb and q2 and 2p coulomb located at $(0, 0, \frac{π}{k}) a n d (0, 0, \frac{3 π}{k}),$ respectively, have the same velocity of 0.5 c $\hat{i}$ (where c is the velocity of light). The ratio of the force acting on charge q1 to q2 is:

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Contributor-Level 10

Force on q₁ :

$F_{q_{1}} = q (V * B) = 4 π (0.5 c \hat{i}) * \frac{B_{0}}{\sqrt[]{2}} (c o s (k z - ω t) \hat{i} + c o s (k z - w t) \hat{j})$

$= 4 π (0.5 c) (\frac{B_{0}}{\sqrt[]{2}}) c o s (k \frac{π}{k}) \hat{k}$

For on q₂:

= $2 π (0.5 c) (\frac{B_{0}}{\sqrt[]{2}}) c o s (k \frac{3 π}{k}) \hat{k}$

So ratio will be 2 : 1

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The electric field in an electromagnetic wave is given by E = $(50 N C^{- 1}) s i n ω (t - x ? / ? c)$ The energy contains in a cylinder of volume V is 5.5 * 10^-12 J. The value of V is________cm³.

(given by $\in_{0} = 8.8 * 1 0^{- 12} C^{2} N^{- 1} m^{- 2})$

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Raj Pandey

Contributor-Level 9

E = (50 N/s) sin (t – x/c)

Energy 5.5 * 10^-12 J., vol v =?

$u = \frac{1}{2} ε_{0} E^{2} \to$ energy density

$? u = \frac{U}{v} \Rightarrow U = u v$

= $\frac{1}{2} ε_{0} E^{2} . v$

$v = \frac{5.5 * 1 0^{- 12} * 2}{8.55 * 2500 * 1 0^{- 12}} * 1 0^{6} c m^{3}$

= 497

$≅ 500 c m^{3}$

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A plane electromagnetic wave with frequency of 30 MHz travels in free space. At particular point in space and time, electric field is 6 V/m. The magnetic field at this pint will be x * 10^-⁸T. The value of x is_______.

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Physics Electromagnetic Waves Electromagnetic Waves

Contributor-Level 10

$B = \frac{E}{c} = \frac{6}{3 * 1 0^{8}} = 2 * 1 0^{- 8} T$

->x = 2

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Electric field in a plane electromagnetic wave is given by

E = 50 sin(500x – 10 * 10¹⁰t) V/m

The velocity of electromagnetic wave in this medium is:

(Given C = speed of light in vacuum)

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Physics Electromagnetic Waves Electromagnetic Waves

Contributor-Level 10

$V = \frac{c o e f f i c i e n t o f t i m e}{c o e f f i c i e n t o f x} = \frac{ω}{k}$

$\Rightarrow V = \frac{10 * 1 0^{10}}{500} = 2 * 1 0^{8} = \frac{2 * c}{3}$

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If E and H represents the intensity of electric field and magnetizing field respectively, then the unit of E/H will be:

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Physics Electromagnetic Waves Electromagnetic Waves

Contributor-Level 10

$\frac{E}{H} = \frac{V o l t / m e t r e}{A m p e r e / m e t r e} = \frac{V o l t}{A m p e r e} = o h m$

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The electric field in a plane electromagnetic wave is given by

$\vec{E} = 200 c o s [(\frac{0.5 * 1 0^{3}}{m}) x (1.5 * 1 0^{11} \frac{r a d}{s} * t)] \frac{V}{m} \hat{j}$

If this wave falls normally on a perfectly reflecting surface having an area of 100 cm². If the radiation pressure exerted by the E.M. wave on the surface during a 10 minute exposure is $\frac{x}{1 0^{9}} \frac{N}{m^{2}} .$ Find the value of x

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Contributor-Level 10

$P = \frac{2 l}{C} P \to$ radiation pressure

$= \frac{2}{C} (\frac{1}{2} ε_{0} E_{0}^{2} C)$

$\begin{array}{l} = ε_{0} E_{0}^{2} \\ = (8.85 * 1 0^{- 12}) * {(200)}^{2} \\ = 354 * 1 0^{- 9} N / m^{2} \end{array}$

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A light beam is described by E = 800 sin $ω (t - \frac{x}{c}) .$ An electron is allowed to move normal to the propagation of light beam with a speed of 3 * 10⁷ ms^-1. What is the maximum magnetic force exerted on the electron?

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Physics Electromagnetic Waves Electromagnetic Waves

Contributor-Level 10

$B_{0} = \frac{E_{0}}{c} = \frac{800}{3 * 1 0^{8}} T$

$F_{m a x} = e v B_{0} = 1.6 * 1 0^{- 19} * 3 * 1 0^{7} * \frac{800}{3 * 1 0^{8}} = 12.8 * 1 0^{- 18} N$

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The electric field in an electromagnetic wave is given by E = 56.5 sin $ω (t - x / c) N C^{- 1} .$ Find the intensity of the wave if it is propagating along x-axis in the free space.

(Given $\in_{0} = 8.85 * 1 0^{- 12} C^{2} N^{- 1} m^{- 2}$ )

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Contributor-Level 10

$E = 56.5 s i n (w (\frac{t - x}{c})) N / c$

$E_{0} = 56.5$

$ε_{0} = 8.85 * 1 0^{- 12}$

C = 3 * 108

l = $\frac{1}{2} ε_{0} E_{0}^{2} C$

$= \frac{1}{2} * 8.85 * 1 0^{- 12} * {(56.5)}^{2} * 3 * 1 0^{8}$

$= 42377.11 * 1 0^{- 4}$

$l = 4.24 w m^{- 2}$

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The electromagnetic waves travel in medium at a speed of 2.0 * 10⁸ m/s. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be:

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