A particle of mass m and charge q is projected into a region having a uniform magnetic field B 0 . Initial velocity ( v 0 ) of the particle is perpendicular to the magnetic field. Apart from the m

Question

A particle of mass m and charge q is projected into a region having a uniform magnetic field $B_{0}$ . Initial velocity $(v_{0})$ of the particle is perpendicular to the magnetic field. Apart from the magnetic force, the particle faces a frictional force which has a magnitude of $f = kv$ where v is instantaneous speed and k is a positive constant. Considering initial time of motion at $t = 0$ . Select the correct option(s):

List - I	List - II
(I) In only uniform electric field	(P) The path may be a straight line
(II) In only uniform magnetic field	(Q) The path may be a parabola
(III) In uniform magnetic and uniform electric field that are both parallel	(R) The path may be a circle
(IV) Subjected to a net force of constant magnitude	(S) The path may be a helix with uniform pitch
	(T) The path may be a helix with non-uniform pitch

TestHub · Accepted Answer

m d t d v ​ = − K v ⇒ v = v 0 ​ e − K t / m Radius: R = qB m v ​ = qB m v 0 ​ ​ e − K t / m Using m v d x d v ​ = − K v ⇒ v = v 0 ​ − m K x ​ So v = 2 v 0 ​ ​ after x = 2 K m v 0 ​ ​ , giving R = 2 qB m v 0 ​ ​ : C and D are correct.

Physics - Magnetism Question with Solution | TestHub

Options:(select one or more)

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