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 t_{1} = 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 t_{1} = 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

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