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A particle of mass m carrying a positive charge q moves simple harmonically along x-axis under the action of a varying electric field E directed along x-axis. The motion of the particle is confined between x = 0 and x = 2l. The angular frequency of the motion is ω. Then, which of the following is correct?
- a)qE = - mω2(x - l)
- b)qE = mω2(x - l)
- c)Electric field to the right of origin is directed along +ve x-axis for all values of x
- d)Electric field to the right of origin is directed along -ve x-axis for all values of x
Correct answer is option 'A'. Can you explain this answer?
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A particle of mass m carrying a positive charge q moves simple harmon...
Explanation:
Simple Harmonic Motion (SHM) Equation:
- In SHM, the acceleration of a particle is directly proportional to its displacement from the mean position and is always directed towards the mean position.
- The equation of motion for a particle undergoing SHM is given by: a = -ω^2x, where a is the acceleration and x is the displacement from the mean position.
Relation with Electric Field:
- In the given scenario, the particle is under the influence of a varying electric field E directed along the x-axis.
- The force experienced by the particle due to the electric field is given by: F = qE, where q is the charge of the particle.
- Equating this force to the mass times acceleration (F = ma), we get: qE = -mω^2x
Confined Motion:
- The motion of the particle is confined between x = 0 and x = 2l.
- The mean position can be taken as x = l (midway between 0 and 2l).
Correct Option:
- The correct option is: qE = - mω^2(x - l).
- This equation represents the relationship between the charge q, electric field E, mass m, angular frequency ω, and displacement x from the mean position l.
Therefore, option A, qE = - mω^2(x - l), is the correct choice as it accurately reflects the dynamics of the particle undergoing simple harmonic motion under the influence of a varying electric field.
Simple Harmonic Motion (SHM) Equation:
- In SHM, the acceleration of a particle is directly proportional to its displacement from the mean position and is always directed towards the mean position.
- The equation of motion for a particle undergoing SHM is given by: a = -ω^2x, where a is the acceleration and x is the displacement from the mean position.
Relation with Electric Field:
- In the given scenario, the particle is under the influence of a varying electric field E directed along the x-axis.
- The force experienced by the particle due to the electric field is given by: F = qE, where q is the charge of the particle.
- Equating this force to the mass times acceleration (F = ma), we get: qE = -mω^2x
Confined Motion:
- The motion of the particle is confined between x = 0 and x = 2l.
- The mean position can be taken as x = l (midway between 0 and 2l).
Correct Option:
- The correct option is: qE = - mω^2(x - l).
- This equation represents the relationship between the charge q, electric field E, mass m, angular frequency ω, and displacement x from the mean position l.
Therefore, option A, qE = - mω^2(x - l), is the correct choice as it accurately reflects the dynamics of the particle undergoing simple harmonic motion under the influence of a varying electric field.
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A particle of mass m carrying a positive charge q moves simple harmon...
Mean position: x = l
F = −k(x − ℓ) ⇒ where k = mω2
or qE = −mω2(x − ℓ) ⇒ At x = ℓ, E = 0
To the right of x = ℓ,E is −ve, so towards left and to the left of x = ℓ E is +ve.
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A particle of mass m carrying a positive charge q moves simple harmonically along x-axis under the action of a varying electric field E directed along x-axis. The motion of the particle is confined between x = 0 and x = 2l. The angular frequency of the motion is ω. Then, which of the following is correct?a)qE = - mω2(x - l)b)qE = mω2(x - l)c)Electric field to the right of origin is directed along +ve x-axis for all values of xd)Electric field to the right of origin is directed along -ve x-axis for all values of xCorrect answer is option 'A'. Can you explain this answer?
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A particle of mass m carrying a positive charge q moves simple harmonically along x-axis under the action of a varying electric field E directed along x-axis. The motion of the particle is confined between x = 0 and x = 2l. The angular frequency of the motion is ω. Then, which of the following is correct?a)qE = - mω2(x - l)b)qE = mω2(x - l)c)Electric field to the right of origin is directed along +ve x-axis for all values of xd)Electric field to the right of origin is directed along -ve x-axis for all values of xCorrect answer is option 'A'. 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 particle of mass m carrying a positive charge q moves simple harmonically along x-axis under the action of a varying electric field E directed along x-axis. The motion of the particle is confined between x = 0 and x = 2l. The angular frequency of the motion is ω. Then, which of the following is correct?a)qE = - mω2(x - l)b)qE = mω2(x - l)c)Electric field to the right of origin is directed along +ve x-axis for all values of xd)Electric field to the right of origin is directed along -ve x-axis for all values of xCorrect answer is option 'A'. 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 particle of mass m carrying a positive charge q moves simple harmonically along x-axis under the action of a varying electric field E directed along x-axis. The motion of the particle is confined between x = 0 and x = 2l. The angular frequency of the motion is ω. Then, which of the following is correct?a)qE = - mω2(x - l)b)qE = mω2(x - l)c)Electric field to the right of origin is directed along +ve x-axis for all values of xd)Electric field to the right of origin is directed along -ve x-axis for all values of xCorrect answer is option 'A'. Can you explain this answer?.
A particle of mass m carrying a positive charge q moves simple harmonically along x-axis under the action of a varying electric field E directed along x-axis. The motion of the particle is confined between x = 0 and x = 2l. The angular frequency of the motion is ω. Then, which of the following is correct?a)qE = - mω2(x - l)b)qE = mω2(x - l)c)Electric field to the right of origin is directed along +ve x-axis for all values of xd)Electric field to the right of origin is directed along -ve x-axis for all values of xCorrect answer is option 'A'. 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 particle of mass m carrying a positive charge q moves simple harmonically along x-axis under the action of a varying electric field E directed along x-axis. The motion of the particle is confined between x = 0 and x = 2l. The angular frequency of the motion is ω. Then, which of the following is correct?a)qE = - mω2(x - l)b)qE = mω2(x - l)c)Electric field to the right of origin is directed along +ve x-axis for all values of xd)Electric field to the right of origin is directed along -ve x-axis for all values of xCorrect answer is option 'A'. 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 particle of mass m carrying a positive charge q moves simple harmonically along x-axis under the action of a varying electric field E directed along x-axis. The motion of the particle is confined between x = 0 and x = 2l. The angular frequency of the motion is ω. Then, which of the following is correct?a)qE = - mω2(x - l)b)qE = mω2(x - l)c)Electric field to the right of origin is directed along +ve x-axis for all values of xd)Electric field to the right of origin is directed along -ve x-axis for all values of xCorrect answer is option 'A'. Can you explain this answer?.
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ample number of questions to practice A particle of mass m carrying a positive charge q moves simple harmonically along x-axis under the action of a varying electric field E directed along x-axis. The motion of the particle is confined between x = 0 and x = 2l. The angular frequency of the motion is ω. Then, which of the following is correct?a)qE = - mω2(x - l)b)qE = mω2(x - l)c)Electric field to the right of origin is directed along +ve x-axis for all values of xd)Electric field to the right of origin is directed along -ve x-axis for all values of xCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice NEET tests.
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