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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 Rand 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?
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
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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.
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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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