1) What is v, the magnitude of the velocity of the proton as it entered the regi

Question

1) What is v, the magnitude of the velocity of the proton as it entered the region containing the magnetic field?  _______m/s

2)  What is R, the radius of curvature of the motion of the proton while it is in the region containing the magnetic field?  ____________m

3)  What is h, the y co-ordinate of the proton as it leaves the region conating the magnetic field?  ______________m

4)  What is Bz, the z-component of the magnetic field?  Note that Bz is a signed number.      ____________T

5)  If the incident velocity v were increased, how would h and (Theta) change, if at all?         

A proton (q = 1.6 X 10^ -19 C, m = 1.67 X 10^ -27 kg) moving with constant velocity enters a region containing a constant magnetic field that is directed along the z-axis at (x,y) = (0,0) as shown. The magnetic field extends for a distance D = 0.53 m in the x-direction. The proton leaves the field having a velocity vector (vx, vy) = (4.6 X 10^5m/s, 1.7 X 10^5m/s). What is v, the magnitude of the velocity of the proton as it entered the region containing the magnetic field? m/s What is R, the radius of curvature of the motion of the proton while it is in the region containing the magnetic field? m What is h, the y co-ordinate of the proton as it leaves the region conating the magnetic field? m What is Bz, the z-component of the magnetic field? Note that Bz is a signed number. T If the incident velocity v were increased, how would h and (Theta) change, if at all?

Explanation / Answer

q = 1.6 X 10^-19 C, m = 1.67 X 10^-27 kg, D = 0.53m,

(vx, vy) = (4.6 X 10^5 m/s, 1.7 X 10^5 m/s).

1) What is v, the magnitude of the velocity of the proton as it entered the region containing the magnetic field?
v = sqrt(vx^2 + vy^2) = 4.9040799341 X 10^5 m/s

2) What is R, the radius of curvature of the motion of the proton while it is in the region containing the magnetic field?
R = D/sin(theta), where tan(theta) = vy/vx

theta = 20.2825590889

R= 0.53 / sin 20.28
R = 1.52891903828m

3) What is h, the y co-ordinate of the proton as it leaves the region conating the magnetic field?
R - h = D/tan(theta) = D*vx/vy = 1.43411764706 m

so h =0.09478235294m

4) What is Bz, the z-component of the magnetic field? Note that Bz is a signed number.
Bz = mv/(qR) = 4.08*10^-3 T

5) If the incident velocity v were increased, how would h and ? change, if at all?
h would decrease and ? would increase

If the velocity were increased, the radius of curvature would increase by the same factor since R is proportional to v. If the radius of curvature increases, the angle through which the particle bends in a distance D also decreases. If the angle decreases, then the displacement h also decreases.

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.