Question

A charged particle of mass m = 4.6X10^-8 kg, moving with constant velocity in the y-direction enters a region containing a constant magnetic field B = 2.3T aligned with the positive z-axis as shown. The particle enters the region at (x,y) = (0.79 m, 0) and leaves the region at (x,y) = 0, 0.79 m a time t = 409 μs after it entered the region.

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

2. What is F_x, the x-component of the force on the particle at a time t₁ = 136.3 μs after it entered the region containing the magnetic field.

3. What is F_y, the y-component of the force on the particle at a time t₁ = 136.3 μs 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.

Answer 1

Solution:-

m = 4.6 * 10^-8 kg
B = 2.3 T
r = 0.79 m
t = 409 us
t1 = 136.3 us

(1)
v = s*(π/2)/t
v = (0.79 * π/2)/ (409* 10^-6)
v = 3032.52 m/s

(2)
Fx = - m*v^2/r * cos(v*t1/r)
Fx = - (4.6 * 10^-8 * 3032.52^2) / 0.79) * cos((3032.52*136.3*10^-6)/0.79)
Fx = - 0.535 * cos(0.522)
Fx = - 0.535 N

(3)
Fy = m*v^2/r * sin(v*t1/r)
Fy = 0.535 * sin(0.522)
Fy = 4.87*10^-3 N

(4)

F = q*v*B
m*v^2/r = q*v*B
m*v/r = q*B
q = (4.6 * 10^-8 * 3032.52)/(0.79 * 2.3)
q = 7.68 * 10^-5 C
q = - 76.8 uC