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Electron of mass m and charge e is travelling with a speed ν along a circular path of radius r at right angles to a uniform magnetic field B. If the speed of the electron is doubled and the magnetic field is halved, the resulting path would have a radius
  • a)
    4 r
  • b)
    2 r
  • c)
    r/4
  • d)
    r/2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Electron of mass m and charge e is travelling with a speed ν along a c...
Explanation:

Given:
- Mass of electron (m) = m
- Charge of electron (e) = e
- Speed of electron (v) = ν
- Radius of circular path (r) = r
- Magnetic field (B) = B

Formula:
The force experienced by a charged particle moving in a magnetic field is given by the formula:
F = evB

Centripetal Force:
The centripetal force required to keep the electron in a circular path is provided by the magnetic force. Therefore,
evB = mv^2/r
This implies r = mv/(eB)

When speed is doubled and magnetic field is halved:
- New speed (v') = 2v
- New magnetic field (B') = B/2

Radius of the new path:
r' = m(2v)/(e(B/2))
r' = 4mv/(eB)
r' = 4r
Therefore, the resulting path would have a radius 4r, which corresponds to option 'A'.
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Electron of mass m and charge e is travelling with a speed ν along a circular path of radius r at right angles to a uniform magnetic field B. If the speed of the electron is doubled and the magnetic field is halved, the resulting path would have a radiusa)4 rb)2 rc)r/4d)r/2Correct answer is option 'A'. Can you explain this answer?
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