Properties of EM Waves

Practice Questions:

Question 1: easy

In an electromagnetic wave, (travelling in vacuum) \(E = 1.2 \sin(2 \times 10^6 t – kx)\text{ N/C}\). Find the value of maximum intensity of magnetic field:

1. \(4 \times 10^{-8}\text{ A/m}\)

2. \(\frac{10^{-3}}{\pi}\text{ A/m}\)

3. \(4 \times 10^{-9}\text{ A/m}\)

4. \(\frac{10^{-2}}{\pi}\text{ A/m}\)

View Answer

Maximum magnetic field \(B_0 = \frac{E_0}{c} = \frac{1.2}{3 \times 10^8} = 4 \times 10^{-9}\text{ T}\). The intensity of magnetic field is \(H_0 = \frac{B_0}{\mu_0} = \frac{4 \times 10^{-9}}{4\pi \times 10^{-7}} = \frac{10^{-2}}{\pi}\text{ A/m}\).

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Question 2: easy

For a plane electromagnetic wave propagating in \(x\)-direction, which one of the following combination gives the correct possible directions for electric field (\(vec{E}\)) and magnetic field (\(vec{B}\)) respectively?

1. \(-\hat{j} + \hat{k}, -\hat{j} + \hat{k}\)

2. \(\hat{j} + \hat{k}, \hat{j} + \hat{k} \)

3. \(-\hat{j} + \hat{k}, -\hat{j} - \hat{k}\)

4. \(\hat{j} + \hat{k}, -\hat{j} - \hat{k} \)

View Answer

The direction of propagation of an electromagnetic wave is given by the cross product \(vec{E} \times \vec{B}\). For wave propagation along the positive \(x\)-direction, the cross product must yield a positive \(hat{i}\) vector. Using option C, \((-\hat{j} + \hat{k}) \times (-\hat{j} - \hat{k}) = \hat{j}\times\hat{k} - \hat{k}\times\hat{j} = 2\hat{i}\), which satisfies this condition.

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Question 3: easy

Match List-I with List-II.

List-I (Types of EM waves)
a. Infrared rays
b. Microwaves
c. UV rays
d. Gamma rays

List-II (Application)
(i) Water purifier
(ii) Remote switches
(iii) Used in medicine to destroy cancer cells
(iv) Cooking

Choose the correct option:

1. a(ii), b(iii), c(iv), d(i)

2. a(i), b(ii), c(iii), d(iv)

3. a(ii), b(iv), c(i), d(iii)

4. a(iii), b(i), c(ii), d(iv)

View Answer

Infrared is used in remote switches (a-ii); Microwaves for cooking (b-iv); UV rays for water purification (c-i); and Gamma rays in cancer cell destruction (d-iii).

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Question 4: easy

Match column I with column II.

| Column-I (Types of EM waves) | Column-II (Production) |

| A. Infra-red | P. Rapid vibration of electrons in aerials |

| B. Radio | Q. Electrons in atoms emit light when they move from higher to lower energy level. |

| C. Light | R. Klystron valve |

| D. Microwave | S. Vibration of atoms and molecules |

Choose the correct match from the options given below:

1. A-P, B-R, C-S, D-Q

2. A-S, B-P, C-Q, D-R

3. A-Q, B-P, C-S, D-R

4. A-S, B-R, C-P, D-Q

View Answer

Infrared waves are produced by molecular vibrations (A-S). Radio waves by accelerating charges in aerials (B-P). Light waves by atomic transitions (C-Q). Microwaves by klystron/magnetron valves (D-R).

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Question 5: easy

For a plane EM wave propagating in x-direction, which one of the following combination gives the correct possible directions for electric field (\(\vec{E}\) ) and magnetic field (\(\vec{B}\) ) respectively?

1. \(-\hat{j} + \hat{k}, -\hat{j} + \hat{k}\)

2. \(\hat{j} + \hat{k}, \hat{j} + \hat{k}\)

3. \(-\hat{j} + \hat{k}, -\hat{j} - \hat{k}\)

4. \(\hat{j} + \hat{k}, -\hat{j} - \hat{k}\)

View Answer

The direction of propagation of an electromagnetic wave is along \(\vec{E} \times \vec{B}\). Here, \((-\hat{j} + \hat{k}) \times (-\hat{j} - \hat{k}) = 2\hat{i}\), which points in the positive x-direction.

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Question 6: easy

Speed of EM wave in free space is given by (where symbols have their usual meaning)

1. \( c = \frac{\varepsilon_0}{\mu_0} \)

2. \( c = \sqrt{\mu_0 \varepsilon_0} \)

3. \( c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \)

4. \( c = \sqrt{\frac{\mu_0}{\varepsilon_0}} \)

View Answer

From Maxwell's electromagnetic theory, the speed of light \( c \) in vacuum is determined by the electric permittivity \( \varepsilon_0 \) and magnetic permeability \( \mu_0 \) of free space through the relation \( c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \).

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Question 7: easy

Assertion (A): When cooking in microwave ovens, metal containers are used.

Reason (R): Energy of microwaves can be easily transferred to the food through metal.

1. Both (A) \(&\) (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) \(&\) (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

Metal containers reflect microwaves and are not used in microwave ovens. Microwaves heat food by interacting with water molecules, not through metal. Thus, both assertion and reason are false.

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Question 8: easy

Assertion (A): Infrared waves are often called heat waves.

Reason (R): Infrared waves vibrate not only electrons but entire atoms or molecules.

1. Both (A) \(&\) (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) \(&\) (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

Infrared waves are absorbed by molecules, increasing their vibrational and rotational energy, which manifests as heat. Thus, both A and R are true, and R explains A.

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Question 9: easy

Assertion (A): Electromagnetic waves cannot penetrate through a perfect conductor and hence are totally reflected.

Reason (R): The speed of electromagnetic waves in any dielectric medium is less as compared to vacuum.

1. Both (A) \(&\) (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) \(&\) (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

A perfect conductor contains free charges that rapidly reorient to cancel the incident electric field, causing total reflection. The speed of EM waves in a dielectric is slower than in vacuum due to the interaction with the medium's polarization. Both statements are true, but R does not explain A.

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Question 10: easy

Assertion (A): Electromagnetic radiations like UV, visible and IR coming from Sun towards earth’s surface can’t be trapped by earth’s magnetic field where as cosmic rays coming towards earth’s surface are trapped by the magnetic field of earth.

Reason (R): Electromagnetic wave doesn’t contain any live charge where the cosmic rays is a huge storage of charged particle.

1. Both (A) \(&\) (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) \(&\) (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

Electromagnetic waves consist of photons and carry no charge, hence they are unaffected by magnetic fields. Cosmic rays are composed of charged particles, which experience a Lorentz force in the Earth's magnetic field, causing them to be trapped or deflected. Thus, R correctly explains A.

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