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Two particles of equal charges after being accelerated through the same potential difference enter in a uniform transverse magnetic field and describe circular paths of radii R1 and R2. Then the ratio of their respective masses (M1/M2) is
- a)R1/R2
- b)(R1/R2)2
- c)R2/R1
- d)(R2/R1)2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two particles of equal charges after being accelerated through the sam...
And Bqv = Mv2/R Or
Using (i)or
∴ M ∝ R2 (∵ B, q and V are same for the given two particles)
Hence (M1/M2) = (R1/R2)2
Most Upvoted Answer
Two particles of equal charges after being accelerated through the sam...
Explanation:
Given:
- Two particles of equal charges
- Accelerated through the same potential difference
- Enter in a uniform transverse magnetic field
- Describe circular paths of radii R1 and R2
To find:
- The ratio of their respective masses (M1/M2)
Formula:
The centripetal force for a charged particle moving in a magnetic field is given by the formula:
F = qvB
The centripetal force is also given by the formula:
F = mv²/R
Where:
- F is the centripetal force
- q is the charge of the particle
- v is the velocity of the particle
- B is the magnetic field
- m is the mass of the particle
- R is the radius of the circular path
Derivation:
- Since the particles have the same charge and are accelerated through the same potential difference, the magnitude of their velocities (v1 and v2) will be the same.
- Therefore, the centripetal forces for both particles will be the same.
- Equating the two formulas for centripetal force:
qv1B = mv1²/R1
qv2B = mv2²/R2
- Dividing the second equation by the first equation:
(v2/v1) = (m2/m1) * (R1/R2)
- Since (v2/v1) = 1 (as the velocities are the same), the equation simplifies to:
1 = (m2/m1) * (R1/R2)
- Rearranging the equation:
(m2/m1) = (R1/R2)²
Therefore, the ratio of their respective masses is equal to the square of the ratio of their radii. Hence, the correct answer is option 'B' (R1/R2)^2.
Given:
- Two particles of equal charges
- Accelerated through the same potential difference
- Enter in a uniform transverse magnetic field
- Describe circular paths of radii R1 and R2
To find:
- The ratio of their respective masses (M1/M2)
Formula:
The centripetal force for a charged particle moving in a magnetic field is given by the formula:
F = qvB
The centripetal force is also given by the formula:
F = mv²/R
Where:
- F is the centripetal force
- q is the charge of the particle
- v is the velocity of the particle
- B is the magnetic field
- m is the mass of the particle
- R is the radius of the circular path
Derivation:
- Since the particles have the same charge and are accelerated through the same potential difference, the magnitude of their velocities (v1 and v2) will be the same.
- Therefore, the centripetal forces for both particles will be the same.
- Equating the two formulas for centripetal force:
qv1B = mv1²/R1
qv2B = mv2²/R2
- Dividing the second equation by the first equation:
(v2/v1) = (m2/m1) * (R1/R2)
- Since (v2/v1) = 1 (as the velocities are the same), the equation simplifies to:
1 = (m2/m1) * (R1/R2)
- Rearranging the equation:
(m2/m1) = (R1/R2)²
Therefore, the ratio of their respective masses is equal to the square of the ratio of their radii. Hence, the correct answer is option 'B' (R1/R2)^2.
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Two particles of equal charges after being accelerated through the same potential difference enter in a uniform transverse magnetic field and describe circular paths of radii R1and R2. Then the ratio of their respective masses (M1/M2) isa)R1/R2b)(R1/R2)2c)R2/R1d)(R2/R1)2Correct answer is option 'B'. Can you explain this answer?
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Two particles of equal charges after being accelerated through the same potential difference enter in a uniform transverse magnetic field and describe circular paths of radii R1and R2. Then the ratio of their respective masses (M1/M2) isa)R1/R2b)(R1/R2)2c)R2/R1d)(R2/R1)2Correct 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 Two particles of equal charges after being accelerated through the same potential difference enter in a uniform transverse magnetic field and describe circular paths of radii R1and R2. Then the ratio of their respective masses (M1/M2) isa)R1/R2b)(R1/R2)2c)R2/R1d)(R2/R1)2Correct 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 Two particles of equal charges after being accelerated through the same potential difference enter in a uniform transverse magnetic field and describe circular paths of radii R1and R2. Then the ratio of their respective masses (M1/M2) isa)R1/R2b)(R1/R2)2c)R2/R1d)(R2/R1)2Correct answer is option 'B'. Can you explain this answer?.
Two particles of equal charges after being accelerated through the same potential difference enter in a uniform transverse magnetic field and describe circular paths of radii R1and R2. Then the ratio of their respective masses (M1/M2) isa)R1/R2b)(R1/R2)2c)R2/R1d)(R2/R1)2Correct 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 Two particles of equal charges after being accelerated through the same potential difference enter in a uniform transverse magnetic field and describe circular paths of radii R1and R2. Then the ratio of their respective masses (M1/M2) isa)R1/R2b)(R1/R2)2c)R2/R1d)(R2/R1)2Correct 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 Two particles of equal charges after being accelerated through the same potential difference enter in a uniform transverse magnetic field and describe circular paths of radii R1and R2. Then the ratio of their respective masses (M1/M2) isa)R1/R2b)(R1/R2)2c)R2/R1d)(R2/R1)2Correct answer is option 'B'. Can you explain this answer?.
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