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 .

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)

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.

MEDIUM

Earn 100

List the consequences of the displacement current.

Important Questions on Electromagnetic Waves

EASY

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

What is displacement current? Write the expression for Ampere-Maxwell law.

EASY

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

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?

HARD

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

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?

EASY

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

State Maxwell's electromagnetic wave theory related to light. The peak value of magnetic field in a progressive electromagnetic wave is

1.5 \times 10^{- 8} tesla

. Find peak value of electric field.

(c = 3 \times 10^{8} \frac{m}{s})

HARD

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

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

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

What do you mean by displacement current. Write its expression.

HARD

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

Match the following and rewrite:

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

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

What is displacement current? Why it is necessary?

EASY

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

In case of charging of a capacitor if

I_{C}

and

I_{D}

be the conduction current and displacement current then at any instant

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

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}]

EASY

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

Write Maxwell's generation of Ampere's circuit law. Show that in the process of charging a capacitor, the current produced within the plates of the capacitor is

i = \in_{0} \frac{{dϕ}_{g}}{dt}

, where

ϕ_{g}

is the electric flux produced during the charging of the capacitor plates.

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

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

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

What is displacement current? Give the expression for it.

EASY

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

What is displacement current and write the modified Ampere's circuital law.

EASY

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

The charging current of a capacitor is

0.6 A

. What is the displacement current across its plates?

EASY

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

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

EASY

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

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})

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

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___

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

The charging current for a capacitor at any instant is

0.78 A

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

EASY

Physics>Electricity and Magnetism>Electromagnetic Waves>Displacement Current

A parallel plate capacitor of capacitance

20 μ F

is being charged by a voltage source whose potential is changing at the rate of

3 V s^{- 1}

. The conduction current through the connecting wires, and the displacement current through the plates of the capacitor would be, respectively:

List the consequences of the displacement current.

Important Questions on Electromagnetic Waves

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