The magnetic field in a plane electromagnetic wave is B y = 2 × 10 - 7 sin 0 . 5 × 10 3 x + 1 . 5 × 10 11 t Tesla . What is the wavelength and frequency of the wave?

Given the magnetic field B y = 2 × 10 - 7 sin 0 . 5 × 10 3 x + 1 . 5 × 10 11 t Tesla Comparing it with the standard equation of the magnetic field B = B 0 sin kx + ωt Tesla , We have the propagation constant, k = 2 π λ = 0 . 5 × 10 3 or λ = 2 × 3 . 14 0 . 5 × 10 3 = 1 . 256 × 10 - 2 m ..............(A) By comparison, the angular velocity is ω = 2 πν = 1 . 5 × 10 11 rad / s , so we get, The frequency, ν = ω 2 π = 1 . 5 × 10 11 2 × 3 . 14 = 2 . 39 × 10 11 Hz .................................(B)

A plain EM wave moving with a velocity 3 × 10 8 ms - 1 has an electric field which oscillates sinusoidally with a frequency 2 × 10 12 Hz and amplitude 48 V / m . What is the amplitude of the oscillating magnetic field?

Given the velocity of the EM wave c = 3 × 10 8 m / s The amplitude of the electric field = 48 Vm - 1 . As we know that the velocity of an electromagnetic wave is given by , c = E B , where E = amplitude of the electric field vector and B = amplitude of the magnetic field vector. Substituting the given values, we get , 3 × 10 8 = 48 B or B = 48 V / m 3 × 10 8 m / s = 1 . 6 × 10 - 7 T . Hence, the amplitude of the magnetic field is 1 . 6 × 10 - 7 T .

Match the following and rewrite: 1 ∮ E → . d A → 1 μ o i c 2 ∮ B → . d A → 2 - d ϕ B d t 3 ∮ E → . d l → 3 Q ε o 4 ∮ B → . d l → 4 0

The correct match is written below: 1 ∮ E → . d A → 3 Q ε o 2 ∮ B → . d A → 4 0 3 ∮ E → . d l → 2 - d ϕ B d t 4 ∮ B → . d l → 1 μ o i c Maxwell formulated the above set of equations involving electric and magnetic fields, and their sources, the charge and current densities. The emergence of electromagnetic waves can be expressed using Maxwell's equations.

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According to Maxwell's hypothesis, changing electric field gives rise to

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Important Questions on Electromagnetic Waves

MEDIUM

General Science>Physics>Electromagnetic Waves>Maxwell's Equations

100 Ω

resistance and a capacitor of

100 Ω

reactance are connected in series across a

220 V

source. When the capacitor is

50 %

charged, the peak value of the displacement current is

EASY

General Science>Physics>Electromagnetic Waves>Maxwell's Equations

Dimensions of

ϵ_{0} \frac{d ϕ_{ϵ}}{d t}

are same as that of (symbols have their usual meanings) _________

EASY

General Science>Physics>Electromagnetic Waves>Maxwell's Equations

A parallel plate capacitor with plates of side

1 m

and plate separation

5 cm

is being charged by an external emf

20 \sin (4 π t)

Volts. The displacement current (in Amperes) in the capacitor is

HARD

General Science>Physics>Electromagnetic Waves>Maxwell's Equations

The displacement current of

4.425 μA

is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of

10^{6} V s^{- 1}

. The area of each plate of the capacitor is

40 {cm}^{2}

. The distance between each plate of the capacitor is

x \times 10^{- 3} m

. The value of

x

is ,
(Permittivity of free space,

ε_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}

) _______

MEDIUM

General Science>Physics>Electromagnetic Waves>Maxwell's Equations

A C

voltage

V (t) = 20 \sin ω t

of frequency

50 Hz

is applied to a parallel plate capacitor. The separation between the plates is

2 mm

and the area is

1 m^{2}

. The amplitude of the oscillating displacement current for the applied

A C

voltage is

[Take ε_{0} = 8.85 \times 10^{- 12} F m^{- 1}]

HARD

General Science>Physics>Electromagnetic Waves>Maxwell's Equations

A parallel plate capacitor has two circular plates of radius $R$ each, separated by a distance $d$ . The magnitude of the instantaneous electric field between the plates is given by $E = E_{0} \sin ω t$ , where $E_{0}$ and $ω$ are positive constants. A positive value of $E$ corresponds to the upward direction as shown in the figure.

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At $t = 0$ , the displacement current between the plates is

EASY

General Science>Physics>Electromagnetic Waves>Maxwell's Equations

A parallel plate capacitor of plate dimensions

2 m \times 2 m

is being charged by a current of

2 A .

In the region between the plates, the charging current produces a uniform electric field

\vec{E}

perpendicular to the plates. The rate of change of the electric field strength with time

(\frac{d E}{d t})

HARD

General Science>Physics>Electromagnetic Waves>Maxwell's Equations

The magnetic field in a plane electromagnetic wave is $B_{y} = 2 \times 10^{- 7} \sin (0.5 \times 10^{3} x + 1.5 \times 10^{11} t) Tesla$ . What is the wavelength and frequency of the wave?

MEDIUM

General Science>Physics>Electromagnetic Waves>Maxwell's Equations

A capacitor of capacitance

C

, is connected across an ac source of voltage

V

, given by

V = V_{0} \sin (ω t)

. The displacement current between the plates of the capacitor would then be given by___

HARD

General Science>Physics>Electromagnetic Waves>Maxwell's Equations

Seawater at a frequency $f = 9 \times 10^{2} Hz$ , has permittivity $ε = 80 ε_{0}$ and resistivity $ρ = 0.25 Ω m$ . Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source $V (t) = V_{0} \sin (2 π f t)$ . Then the conduction current density becomes $10^{x}$ times the displacement current density after time $t = \frac{1}{800} s .$ The value of $x$ is _______

(Given $: \frac{1}{4 π ε_{0}} = 9 \times 10^{9} N m^{2} C^{- 2})$

EASY

General Science>Physics>Electromagnetic Waves>Maxwell's Equations

A plain EM wave moving with a velocity $3 \times 10^{8} {ms}^{- 1}$ has an electric field which oscillates sinusoidally with a frequency $2 \times 10^{12} Hz$ and amplitude $48 V / m$ . What is the amplitude of the oscillating magnetic field?

MEDIUM

General Science>Physics>Electromagnetic Waves>Maxwell's Equations

The charging current for a capacitor at any instant is

0.78 A

. The displacement current across the capacitor plates at that instant is

HARD

General Science>Physics>Electromagnetic Waves>Maxwell's Equations

Match the following and rewrite:

$(1) \oint \vec{E} . \vec{d A}$	$(1) μ_{o} i_{c}$
$(2) \oint \vec{B} . \vec{d A}$	$(2) - \frac{d ϕ_{B}}{d t}$
$(3) \oint \vec{E} . \vec{d l}$	$(3) \frac{Q}{ε_{o}}$
$(4) \oint \vec{B} . \vec{d l}$	$(4) 0$

HARD

General Science>Physics>Electromagnetic Waves>Maxwell's Equations

A long wire of radius $R$ is made of two different metals, depositing one metal over the other. The inner core occupies the region $r < R$ and the outer region $R < r \leq 2 R$ . Because of difference in the conductivity of the two wires, only $10 %$ of the total current flows through the inner core and the balance through the second metal. The current density in each metal is constant.

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