A charged particle of mass 6.00 mg moves with a speed of 4.00 km/s in a direction that makes an angle of 37o above the positive x-axis. At the instant it enters a magnetic field of 5.00 mT which is in the positive x direction (+i), it experiences an acceleration of 8.00 m/s2 in the positive z direction (+k). What is the charge of the particle?

Explanation:

mass of charged particle m = 6 x 10⁻³ kg .

speed of particle   v  = 4 x 10³ m /s

speed of particle perpendicular to magnetic field = v sin37

= 4 x 10³ sin37

= 2.41 x 10³ m / s

Force on charged particle

= B q v , B is magnetic field , q is charge on particle and v is velocity perpendicular to B

Force = ma

= 6 x 10⁻³ x 8

= 48 x 10⁻³

Force = Bqv

48 x 10⁻³ = 5 x 10⁻³ q x  2.41 x 10³

q = 48 x 10⁻³  / (5 x 2.41)

= 3.98 x 10⁻³C.

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