A charged particle of mass m = 7.5X10 -8 kg, moving with constant velocity in th

Question

A charged particle of mass m = 7.5X10-8 kg, moving with constant velocity in the y-direction enters a region containing a constant magnetic field B = 1.9T aligned with the positive z-axis as shown. The particle enters the region at (x,y) = (0.5 m, 0) and leaves the region at (x,y) = 0, 0.5 m a time t = 494 ?s after it entered the region.

1)

With what speed v did the particle enter the region containing the magnetic field?

2)

What is Fx, the x-component of the force on the particle at a time t1 = 164.7 ?s after it entered the region containing the magnetic field.

3)

What is Fy, the y-component of the force on the particle at a time t1 = 164.7 ?s after it entered the region containing the magnetic field.

4)

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

Explanation / Answer

a)

since the particle flows in circular path

L=piR/2 =pi*0.5/2 =0.785 m

V=L/t =0.785/(494*10^-6)

V=1589.07 m/s

b)

X=theta =Wt =(V/R)t

X =(1589.07/0.5)*164.7*10^-6

X=0.5234 rad =0.5234*(180/pi)

X=30 degrees

F=mV^2/R =(7.5*10^-8)(1589.07)^2/0.5

F=0.379 N

Fx =Fcos(x) =0.379*cos30

Fx =0.328 N

c)

Fy=Fsin(x) =0.379*sin30

Fy =0.1895 N

d)

F=QVB

Q=F/VB=0.379/(1589.07*1.9)

Q=125.53 uC

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