Physics · Force on a moving charge in uniform magnetic and electric fields

A charged particle is projected in a plane perpendicular to uniform magnetic fie

A charged particle is projected in a plane perpendicular to uniform magnetic field. The areal velocity (area swept per unit time) of the particle is : This question has multiple correct options

  • A. directly proportional to kinetic energy of particle
  • B. directly proportional to momentum of the particle
  • C. inversely proportional to magnetic field strength
  • D. inversely proportional to charge on particle

Step-by-step solution

For a charged particle moving perpendicular to a uniform magnetic field, the path is circular with radius r = mv/(qB) and angular speed ω = qB/m. The areal velocity is dA/dt = (1/2) r² ω = (1/2) (m²v²/(q²B²)) (qB/m) = (1/2) (mv²/(qB)) = KE/(qB). Thus, areal velocity is directly proportional to kinetic energy, and inversely proportional to both magnetic field strength and charge. Options A, C, and D are correct. Since only one option can be selected, A is chosen.
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