4) What is q, the charge of the particle? Be sure to include the correct sign. A

Question

4) What is q, the charge of the particle? Be sure to include the correct sign. A charged particle of mass m 5.4 X 10^-8 kg, moving with constant velocity in the y-direction enters a region containing a constant magnetic field B 1 = 1.1 T aligned with the positive z-axis as shown. The particle enters the region at (x, y) (0.69 m, 0) and leaves the region at (x, y) = 0, 0.69 m a time t = 408 mus after it entered the region. 1) With what speed y did the particle enter the region containing the magnetic field? 2) What is F, the x-component of the force on the particLe at a time t1 136 ps after it entered the region containing the magnetic field. 3) What is F, the y-component of the force on the particle at a time t1 = 136 ps after it entered the region containing the magnetic fieLd.

Explanation / Answer

w = (pi/2)/t = (3.14)/(2*408e-6) = 3848.04 rad/s

distance = pi*r/2 = (3.14*0.69)/2 = 1.0833

1) speed = distane /time = 1.0833/(408e-6) = 2655.15 m/s

2)

angle at t1 = 136us is theta = 3848.04*136e-6 = 29.9 degree = 30 (nearly)

centripetal force Fc = m*v^2/r = (5.4e-8*2655.15*2655.15)/0.69 = 0.5517 N

Fx = -Fc*cos30 = -0.478 N <<<-------answer

3) Fy = -Fc*sin30 = 0.27585 N <---------answer

4)

Fc = Fb

Fc = q*v*B

q = Fc/(v*B) = 0.5517/(2655.15*1.1)

q = 188.9 uC <---------answer

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