A charged particle of mass m = 6X10 -8 kg, moving with constant velocity in the

Question

A charged particle of mass m = 6X10-8 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) = (0.96 m, 0) and leaves the region at (x,y) = 0, 0.96 m a time t = 756 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 Fx, the x-component of the force on the particle at a time t1 = 252 s after it entered the region containing the magnetic field.N

3)What is Fy, the y-component of the force on the particle at a time t1 = 252 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

Explanation / Answer

1)

v = s / t

v = (d*pi/2) / t

v = (0.96*3.14/2) / (756 x 10^-6)

v = 1994 m/s

2)

s1 = d*(theta)1 = vt1

(theta)1 = vt1 / d

(theta)1 = (1994 x 252 x 10^-6) / 0.96 = 0.523

Fx = -[mv^2 / d]*cos(theta)1

Fx = -{[6 x 10^-8 x 1994^2] / 0.96}*cos(0.523)

Fx = -0.2485 N

3)

Fy = -[mv^2 / d]*sin(theta)1

Fy = -{[6 x 10^-8 x 1994^2] / 0.96}*sin(0.523)

Fy = -0.0022 N

4)

q = mv / dB

q = (6 x 10^-8 x 1994) / (0.96 x 1.3)

q = -95.87 uC

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