Question

2. A particle, having a mass of 4.5 mg and a charge of 3.2 uC, is traveling eastward with a velocity of 3.0 km/s. It enters a region with a magnetic field that is perpendicular to the particle and suddenly has an acceleration of 9.2 m/s2 upward. (A) What is the magnitude and direction of the magnetic field? (B) Describe the path of the particle quantitatively and qualitatively (i.e. give a description of the particle's path along with any relevant values).

Answer 1

We have given the mass and charge of a particle are 4.5mg and 3.2uC respectively. Moving eastward with velocity = 3000m/s.

As it eneterd into the region of magnetic that is perpendicular to particle's velocity, the magnetic Lorentz force will act on the charged particle which will provide the Centripetal force in order to move in circular orbits.

F = Fm

m(ac) = quB

m(a) B =- qu

4.5 x 10-6 x 9.2 3.2 x 10-6 X 3000 4.1325 x 10-3 T

if you consider the particle is moving eastward and the force acted upward along North then magnetic field must be into the page of the paper (as shown in the figure) from the right hand product rule.

B). As the magnetic field is perpendicular to velocity of the charged particle the particle will move in circular orbit.

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IN acc. acc. a force fm= q (5x5) V3 B (Magnitic field) should be into the page- qXB = muk qB=mv - I MV R lmvo I EB Rading of Cirahcrbit mY - 4.5x16*x 3000 3 3.2x106x 4.135x10 R=1.02.1X106 m ř 1021x103 m ~ 1021 km