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A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly:
- a)1.34 V/m
- b)2.68 V/m
- c)4.02 V/m
- d)5.36 V/m
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A lamp emits monochromatic green light uniformly in all directions. T...
Given:
- A lamp emits monochromatic green light uniformly in all directions.
- The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power.
- The distance from the lamp is 5 m.
To find: The amplitude of the electric field associated with the electromagnetic radiation.
Solution:
1. Calculate the power of the electromagnetic radiation:
The lamp is 3% efficient in converting electrical power to electromagnetic waves. Therefore, the power of the electromagnetic radiation emitted by the lamp can be calculated as:
Power of electromagnetic radiation = 3% of 100 W
= (3/100) x 100 W
= 3 W
2. Calculate the intensity of the electromagnetic radiation:
The intensity of the electromagnetic radiation can be calculated as:
Intensity = Power / (4πr^2)
where r is the distance from the lamp.
Substituting the values, we get:
Intensity = 3 W / (4π x 5^2 m^2)
= 3 / (4π x 25) W/m^2
= 0.0239 W/m^2
3. Calculate the electric field strength:
The electric field strength can be calculated using the formula:
E = √(2I/εc)
where I is the intensity of the electromagnetic radiation, ε is the permittivity of free space, and c is the speed of light in vacuum.
Substituting the values, we get:
E = √(2 x 0.0239 W/m^2 / (8.85 x 10^-12 F/m) x (3 x 10^8 m/s))
= 2.68 V/m
Therefore, the amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp is 2.68 V/m, which is closest to option B.
- A lamp emits monochromatic green light uniformly in all directions.
- The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power.
- The distance from the lamp is 5 m.
To find: The amplitude of the electric field associated with the electromagnetic radiation.
Solution:
1. Calculate the power of the electromagnetic radiation:
The lamp is 3% efficient in converting electrical power to electromagnetic waves. Therefore, the power of the electromagnetic radiation emitted by the lamp can be calculated as:
Power of electromagnetic radiation = 3% of 100 W
= (3/100) x 100 W
= 3 W
2. Calculate the intensity of the electromagnetic radiation:
The intensity of the electromagnetic radiation can be calculated as:
Intensity = Power / (4πr^2)
where r is the distance from the lamp.
Substituting the values, we get:
Intensity = 3 W / (4π x 5^2 m^2)
= 3 / (4π x 25) W/m^2
= 0.0239 W/m^2
3. Calculate the electric field strength:
The electric field strength can be calculated using the formula:
E = √(2I/εc)
where I is the intensity of the electromagnetic radiation, ε is the permittivity of free space, and c is the speed of light in vacuum.
Substituting the values, we get:
E = √(2 x 0.0239 W/m^2 / (8.85 x 10^-12 F/m) x (3 x 10^8 m/s))
= 2.68 V/m
Therefore, the amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp is 2.68 V/m, which is closest to option B.
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Community Answer
A lamp emits monochromatic green light uniformly in all directions. T...
Wavelength of monochromatic green light
= 5.5 × 10–5 cm
Now, half of this intensity (I) belongs to electric field and half of that to magnetic field, therefore,
∴ E0 = 2.68 V/m
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A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly:a)1.34 V/mb)2.68 V/mc)4.02 V/md)5.36 V/mCorrect answer is option 'B'. Can you explain this answer?
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A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly:a)1.34 V/mb)2.68 V/mc)4.02 V/md)5.36 V/mCorrect answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly:a)1.34 V/mb)2.68 V/mc)4.02 V/md)5.36 V/mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly:a)1.34 V/mb)2.68 V/mc)4.02 V/md)5.36 V/mCorrect answer is option 'B'. Can you explain this answer?.
A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly:a)1.34 V/mb)2.68 V/mc)4.02 V/md)5.36 V/mCorrect answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly:a)1.34 V/mb)2.68 V/mc)4.02 V/md)5.36 V/mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly:a)1.34 V/mb)2.68 V/mc)4.02 V/md)5.36 V/mCorrect answer is option 'B'. Can you explain this answer?.
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