Question

A point charge with a mass of 1.81 ng and a charge of +1.22 ?C moves in the x-y plane with a velocity of 3.00 x 104 m/s in a direction 15° above the +x-axis. At time t=0, the point charge enters a uniform magnetic field of strength 1.25 T that points in the +x-direction.Assume that the point charge remains immersed in the uniform magnetic field after time t=0.

a) What is the magnitude and direction of the magnetic force that the magnetic field exerts on the point charge at time t=0?

b) How does the x-component of the charge’s initial velocity effect the motion of this point charge as it moves through the uniform magnetic field? Does its magnitude change? Does its direction change? Explain your reasoning.

c) How does the y-component of the charge’s initial velocity effect the motion of this point charge as it moves through the uniform magnetic field? Does its magnitude change? Does its direction change? Explain your reasoning.

d) Use your answers from parts 1b & 1c to explain why the path of this point charge is helical (corkscrew-shaped). Explain your reasoning.

e) Determine the radius of the circular part of the point charge’s helical path.

Answer 1

given

m = 1.81 ng = 1.81*10^-9 g

q = 1.22 micro C
v = 3.00*10^4 m/s
theta = 15 degrees
B = 1.25 T

a) |F| = q*v*B*sin(theta) (here theta is the angle between v and B)

= 1.22*10^-6*3*10^4*1.25*sin(15)

= 0.0118 N

direction : towards -z axis

b) The x-component of the charge’s initial velocity does not effect the motion of this point charge as it moves through the uniform magnetic field.

Because, magnetic field is along +x axis.

its magnitude does not change.

its direction does not change.

c) The y-component of the charge’s initial velocity effects the motion of this point charge as it moves through the uniform magnetic field.

because, voy and B are perpendicular to each other.

Its magnitude does not change.

Its direction changes, because of magnetic force.

d) because, x-component of velocity remains constant and magnitude of y-component of velocity is also constant. But direction of velocity along y axis always changes.

so, the particle follows a helical path.

e) r = m*voy/(B*q)

= 1.81*10^-9*3*10^4*sin(15)/(1.25*1.22*10^-6)

= 9.21 m