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.
Related MCQs
- Assertion A stationary charged particle in a magnetic field does not experience a force. Reason The force acting on a charged particle does …
- A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected a…
- A charged particle is moving in a uniform magnetic field in a circular path. The energy of the particle is doubled. If the initial radius of…
- An electron is projected into a magnetic field along the lines of force. Then…
- Pick up the correct statements: This question has multiple correct options…