A charged particle of mass m 59X108 kg moving with constant

A charged particle of mass m = 5.9X10^-8 kg, moving with constant velocity in the y-direction enters a region containing a constant magnetic field B = 1.3T aligned with the positive z-axis as shown. The particle enters the region at (x,y) = (0.7 m, 0) and leaves the region at (x,y) = 0, 0.7 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?

m/s

2)

What is F_x, 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.

N

3)

What is F_y, 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.

N

4)

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

C

Solution

given that, m = 5.9*10^-8 kg,

                  B = 1.3 T,

                   r = 0.7 m,

                   t = 494 µs

1)

in this case, period is, t = (2*pi*r/4) / v
so the velocity is,

       v =2*pi*r/(4t) = 2225.82 m/s
2)

The angle turned is ,

    @ = (pi/2)*t1/t = 0.5237 rad

thus, the x-component of force F is,

         Fx = -(mv^2/r)cos@ = -0.3616 N

here, theta is calculated in radians.
3)

the y-component of force F is,

      Fy = -(mv^2/r)sin@ = -0.2088 N
4)

charge is calculated as follows:

   q = mv/(Br) =1.44*10^-4 C = 144 uC
by the right hand rule q is negative, so q = -144 uC