Suppose that the electric field part of an electromagnetic wave in vacuum is E = {(3.1 N/C) cos [(1.8 rad/m) y + (5.4 × 10⁶ rad/s)t]} $\hat{i} .$ What is the wavelength λ?

Solution

Given,
Electric field, E = {(3.1 N/C) cos [(1.8 rad/m) y + (5.4 × 10⁶ rad/s)t]} $\hat{i} .$

Comparing the given equation with the equation
$E = E_{0} \cos (ky + ωt) \overset{⏜}{i}$ a

Therefore, we get

$Amplitude of electric field, E_{0} = 3.1 {NC}^{- 1} Wave vector, k = 1.8 rad m^{- 1} Angular frequency, ω = 5.4 \times 10^{6} rad s^{- 1}$ .

We know that,
$ω = 2 π v$
$\Rightarrow$ $5.4 \times 10^{6} = 2 π v = 2 π \times \frac{c}{λ}$
$\Rightarrow$ $λ = \frac{2 πc}{5.4 \times 10^{8}} = \frac{2 π \times 3 \times 10^{8}}{5.4 \times 10^{8}}$

$= 3.5 m$
which is the required value of wavelength.

Some More Questions From Current Electricity Chapter

What conclusion can you draw from the following observations on a resistor made of alloy manganin?

Current A

Voltage V

Current A

Voltage V

0.2

0.4

0.6

0.8

1.0

2.0

3.94

7.87

11.8

15.7

19.7

39.4

3.0

4.0

5.0

6.0

7.0

8.0

59.2

78.8

98.6

118.5

138.2

158.0

Answer the following questions:
A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?

Answer the following questions:
Is Ohm’s law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm’s law.

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Current Electricity

Suppose that the electric field part of an electromagnetic wave in vacuum is E = {(3.1 N/C) cos [(1.8 rad/m) y + (5.4 × 10⁶ rad/s)t]} $\hat{i} .$ What is the wavelength λ?

Some More Questions From Current Electricity Chapter

What conclusion can you draw from the following observations on a resistor made of alloy manganin?

Current A

Voltage V

Current A

Voltage V

0.2

0.4

0.6

0.8

1.0

2.0

3.94

7.87

11.8

15.7

19.7

39.4

3.0

4.0

5.0

6.0

7.0

8.0

59.2

78.8

98.6

118.5

138.2

158.0

Answer the following questions:
A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?

Answer the following questions:
Is Ohm’s law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm’s law.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Email Address

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For Daily Free Study Material Join wiredfaculty

Current Electricity

Suppose that the electric field part of an electromagnetic wave in vacuum is E = {(3.1 N/C) cos [(1.8 rad/m) y + (5.4 × 106 rad/s)t]}i^. What is the wavelength λ?

Some More Questions From Current Electricity Chapter

What conclusion can you draw from the following observations on a resistor made of alloy manganin? Current A Voltage V Current A Voltage V 0.2 0.4 0.6 0.8 1.0 2.0 3.94 7.87 11.8 15.7 19.7 39.4 3.0 4.0 5.0 6.0 7.0 8.0 59.2 78.8 98.6 118.5 138.2 158.0

Answer the following questions:A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?

Answer the following questions:Is Ohm’s law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm’s law.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Suppose that the electric field part of an electromagnetic wave in vacuum is E = {(3.1 N/C) cos [(1.8 rad/m) y + (5.4 × 10⁶ rad/s)t]} $\hat{i} .$ What is the wavelength λ?

What conclusion can you draw from the following observations on a resistor made of alloy manganin?

Current A

Voltage V

Current A

Voltage V

0.2

0.4

0.6

0.8

1.0

2.0

3.94

7.87

11.8

15.7

19.7

39.4

3.0

4.0

5.0

6.0

7.0

8.0

59.2

78.8

98.6

118.5

138.2

158.0

Answer the following questions:
A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?

Answer the following questions:
Is Ohm’s law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm’s law.