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Electrons at rest are accelerated by a potential of V volt. These electrons enter the region of space having a uniform, perpendicular magnetic induction field B. The radius of the path of the electrons inside the magnetic field is:

Correct answer: B. The radius is proportional to the square root of (2mV/e) divided by the magnetic field B

  • A. The radius is proportional to the square root of the potential V divided by the magnetic field B
  • B. The radius is proportional to the square root of (2mV/e) divided by the magnetic field B
  • C. The radius is directly proportional to the potential V and inversely proportional to the magnetic field B and charge e
  • D. The radius is directly proportional to the magnetic field B and inversely proportional to the square root of the potential V

Explanation

The gain in K.E. of the electron after moving through the potential differenceV = eV = (1/2) m v²⇒ v = √(2 e V / m)⇒ r = mv / eB = (1/B) √(2 m V / e)

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About Electromagnetism

Magnetic flux density and magnetic flux describe the strength of a magnetic field and the field passing through a surface. A charged particle moving through a magnetic field experiences a force perpendicular to its velocity and may follow circular or helical motion, depending on the angle between velocity and field.

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