Physics Electromagnetic Waves

Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of µ?I/π is:

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Contributor-Level 10

Kindly go through the solution

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2 months ago

A plane electromagnetic wave, has frequency of 2.0 * 10¹⁰ Hz and its energy density is 1.02 * 10⁻⁸ J/m³ in vacuum. The amplitude of the magnetic field of the wave is close to (1/(4πε₀) = 9 * 10⁹ Nm²/C² and speed of light = 3 * 10⁸ ms⁻¹):

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Physics Electromagnetic Waves Electromagnetic Waves

Contributor-Level 10

Energy Density = 1/2 B²/µ?
B = √ (2 * µ? * Energy density)
B = √ (2 * 4π * 10? * 1.02 * 10? ) = 160 * 10? = 160nT

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2 months ago

Suppose that intensity of a laser is (315/π) W/m². The rms electric field, in units of V/m associated with this source is close to the nearest integer is (ε₀ = 8.86 * 10⁻¹² C²N⁻¹m⁻²; c = 3 * 10⁸ ms⁻¹)

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Physics Electromagnetic Waves Electromagnetic Waves

Contributor-Level 10

I=½ε? E? ²c ⇒ E? =√ (2I/ε? c)
Erms = E? /√2 = √ (I/ε? c) = √ (315/π / (8.86e-12 * 3e8) = 194

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3 months ago

The quantities x = 1/√(µ₀ε₀), y = E/B and z = 1/CR are defined where C-capacitance, R Resistance, l-length, E-Electric field, B-magnetic field and ε₀, µ₀, - free space permittivity and permeability respectively. Then:

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Physics Electromagnetic Waves Electromagnetic Waves

Contributor-Level 10

x = 1/√ (µ? ε? ) = speed ⇒ [x] = [L¹T? ¹]
y = E/B = speed ⇒ [y] = [L¹T? ¹]
z = l/ (RC) = l/τ ⇒ [z] = [L¹T? ¹]
So, x, y, z all have the same dimensions.

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3 months ago

The correct match between the entries in column I and column II are:

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Physics Electromagnetic Waves Electromagnetic Waves

Contributor-Level 10

Energies of given Radiation can have
The following relation
Eγ-Rays > EX-Rays > Emicrowave > EAM Radiowaves
∴ λγ-Rays < X-Rays < microwave < AM Radiowaves
According to tres.
(a) Microwave → 10? ³ m
(b) Gamma Rays → 10? ¹? m (ii)
(c) AM Radio wve → 100 m (i)
(d) X-Rays → 10? ¹? m

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New answer posted

3 months ago

If the magnetic field in a plane electromagnetic wav is given by $\overset{?}{B} = 3 * 10^{- 8}$ $s i n ? (1.6 * 10^{3} x + 48 * 10^{10} t) j T$ $^{}$ $(^{}^{})$ , then what will be expression for electric field?

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Contributor-Level 10

$m = L, b = R, k = \frac{1}{c}$ (speed of light in vacuum)

$\frac{E_{0}}{B_{0}} = C$

So, $E_{0} = B_{0} C = 3 * 10^{- 8} * 3 * 10^{8} = 9 N / C$

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3 months ago

The electric field of a plane electromagnetic wave is given by

$\vec{E} = E_{0} \frac{\hat{i} + \hat{j}}{\sqrt[]{2}} c o s (k z + ω t)$

At $t = 0$ , a positively charged particle is at the point $(x, y, z) = (0,0, \frac{π}{k})$ . If its instantaneous velocity at $(t = 0)$ is $v_{0} \hat{k}$ , the force acting on it due to the wave is:

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Contributor-Level 10

Electric field at $t = 0$ & $(x, y, z) = (0,0, \frac{π}{k})$ is

$\begin{array}{r} \overset{?}{E} = - (\frac{\hat{i} + \hat{j}}{\sqrt[]{2}}) E_{0} and \overset{?}{F} = \overset{?}{E} q \\ ∴ \overset{?}{F} = - (\frac{\hat{i} + \hat{j}}{\sqrt[]{2}}) q \end{array}$

Which is antiparallel to $(\frac{\hat{i} + \hat{j}}{\sqrt[]{2}})$

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New answer posted

3 months ago

For an electromagnetic wave traveling in free space, the relation between average energy densities due to electric (Ue) and magnetic (Um) fields is :

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Raj Pandey

Contributor-Level 9

Kindly consider the following Image

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New answer posted

3 months ago

A linearly polarized electromagnetic wave in vacuum is E = 3.1 cos[(1.8)z - (5.4 * 10?)t] î N/C. Is incident normally on a perfectly reflecting wall at z = a. Choose the correct option

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Raj Pandey

Contributor-Level 9

Reflected wave will be 3.1cos [1.8z + (5.4*10? )t] î N/C
K = 2π/λ
⇒ 1.8 = 2π/λ
λ = 2π/1.8 = π/0.9 = 10π/9 = (10/9) * 3.14
= 3.48m

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New answer posted

3 months ago

An electromagnetic wave of frequency 5 GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2. Its velocity in the this medium is_____* 10⁷ m/s.

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