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![Page 1: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/1.jpg)
A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that
the only force on the proton is the magnetic force. Explain why the proton will move in a
helical path. Find an expression for the pitch of the helix.
+ B
v
x
y
zBold type denotes vector quantities
![Page 2: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/2.jpg)
Question 1Question 2Question 3Question 4Question 5Question 6Question 7Question 8
Question 9Question 10Question 11
![Page 3: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/3.jpg)
1. Why does the proton feel a magnetic force?
i) Because it has a chargeii) Because it is moving with a velocity which is not parallel to the
magnetic fieldiii) Because it has a mass
A : i onlyB : ii onlyC : iii onlyD : i and ii onlyE : ii and iii only
![Page 4: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/4.jpg)
Choice AIncorrect
In order to feel a magnetic force, a particle must be charged. There is another condition that must be met for the particle to feel a magnetic force.
Think about the following equation:
€
Fmag=q(v ×B) = qvBsinθn
Unit vector perpendicular to v and B
Unit vector perpendicular to v and B
![Page 5: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/5.jpg)
Choice BIncorrect
This is true, because if a particle is moving with a velocity that is parallel to the magnetic field (=0), the particle will not feel a force:
BUT, this is not the only reason that the proton will feel a magnetic force.
€
Fmag=q(v ×B) = qvBsin(0)n = 0Unit vector perpendicular to v and B
Unit vector perpendicular to v and B
![Page 6: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/6.jpg)
Choice CIncorrect
Mass has nothing to do with a particle feeling a magnetic force.
![Page 7: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/7.jpg)
Choice DCorrect
€
Fmag=q(v ×B) = qvBsinθn
Notice that if the charge q of a particle or the angle between the magnetic field and the velocity of the particle is zero, the magnetic force on the particle will be zero.
Unit vector in the direction of the force
Unit vector in the direction of the force
![Page 8: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/8.jpg)
Choice EIncorrect
One reason that the proton feels a magnetic force is because it is moving with a velocity that is not parallel to the magnetic field, but mass has nothing to do with a particle feeling a magnetic force. Try again
![Page 9: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/9.jpg)
• We will break the motion of the proton into components to see the contributions of each.
• Let’s first take a look at the motion of the proton along the x-axis. Notice that the axes are defined on the first slide.
![Page 10: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/10.jpg)
2. Which of the following choices correctly describes the x-component of the proton’s
motion?
A: The proton is accelerating in the x-direction (ax>0)
B: There is no motion in the x-direction.
C: The x-component of the proton’s velocity vx is constant.
![Page 11: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/11.jpg)
Choice AIncorrect
The proton is not accelerating in the x-direction, because the x-component of the magnetic force Fx is zero.
The x-component of the proton’s velocity is parallel to the magnetic field, therefore a force will not be felt by the proton due to the horizontal component of motion.
vy
vx
v
B
€
Fx =qvBsinθ = 0
![Page 12: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/12.jpg)
Choice BIncorrect
Initially, there is motion in the x-direction and the y-direction, because it is stated that the proton is shot with a velocity at an angle to the x-axis. It is not shot directly upwards in the y-direction.
![Page 13: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/13.jpg)
Choice CCorrect
This is true because there is no x-component of magnetic force on the proton.
The x-component of the proton’s velocity is parallel to the magnetic field, therefore a force will not be felt by the proton due to the horizontal component of motion.
€
Fx =qvBsinθ = 0
![Page 14: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/14.jpg)
3. What type of path will the proton follow if only the motion in the x-y plane is
considered?
A: Straight line (Linear)
B: Parabolic
C: Circular
This is due to the horizontal component of the initial
velocity.
![Page 15: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/15.jpg)
Choice ACorrect
If we only consider the motion in the x-y plane, the particle will move with constant velocity in the positive x-direction and will not change directions. This describes a linear path.
![Page 16: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/16.jpg)
Choice BIncorrect
If we only consider the motion in the x-y plane, the particle will move with constant velocity in the positive x-direction and will not change directions. This describes a linear path.
![Page 17: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/17.jpg)
Choice CIncorrect
If we only consider the motion in the x-y plane, the particle will move with constant velocity in the positive x-direction and will not change directions. This describes a linear path.
![Page 18: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/18.jpg)
4. Which of the following choices correctly describes the y-component of the proton’s
motion as it moves through the magnetic field?
A: The proton is accelerating in the y-direction (ay≠0)
B: There is no motion in the y-direction.
C: The y-component of the proton’s velocity vy is constant.
![Page 19: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/19.jpg)
Choice ACorrect
The proton would accelerate in the y-direction because the y-component of velocity causes a magnetic force to be felt by the proton.
Where: ≠0Where: ≠0
€
F =qvBsinθ
F = qv yB
![Page 20: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/20.jpg)
Choice BIncorrect
There is motion in the x-direction and the y-direction because it is stated that the proton is shot with a velocity at an angle to the x-axis. It is not shot horizontally.
![Page 21: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/21.jpg)
Choice CIncorrect
The y-component of the proton’s velocity vy is not constant, because this motion causes a magnetic force to be felt by the proton.
€
F =qvBsinθWhere: ≠0Where: ≠0
![Page 22: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/22.jpg)
5. What type of path will the proton follow if only the motion of the proton in the y-z plane is considered?
A: Straight line (Linear)
B: Parabolic
C: Circular
This is due to the vertical component of the initial
velocity.
![Page 23: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/23.jpg)
Choice AIncorrect
Using the right hand rule we see that the magnetic force on the proton will cause it to travel on a circular path (counterclockwise if looking down the x-axis from the origin).
F
B
v
The force must be centripetal and have constant magnitude to obtain uniform circular motion.
At any instant during the proton’s motion, your middle finger should point down the positive x-axis. and your pointer finger should point in the direction of the y-component of the velocity. This will direct your thumb in the direction of the force that pushes the proton.
At any instant during the proton’s motion, your middle finger should point down the positive x-axis. and your pointer finger should point in the direction of the y-component of the velocity. This will direct your thumb in the direction of the force that pushes the proton.
![Page 24: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/24.jpg)
Choice BIncorrect
Using the right hand rule we see that the magnetic force on the proton will cause it to travel on a circular path (counterclockwise if looking down the x-axis from the origin).
F
B
v
At any instant during the proton’s motion, your middle finger should point down the positive x-axis. and your pointer finger should point in the direction of the y-component of the velocity. This will direct your thumb in the direction of the force that pushes the proton.
At any instant during the proton’s motion, your middle finger should point down the positive x-axis. and your pointer finger should point in the direction of the y-component of the velocity. This will direct your thumb in the direction of the force that pushes the proton.
The force must be centripetal and have constant magnitude to obtain uniform circular motion.
![Page 25: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/25.jpg)
Choice CCorrect
If we only consider the motion of the proton in the y-z plane due to its initial vertical motion, the proton’s path would be circular.
![Page 26: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/26.jpg)
6. What type of path do you get if you combine the contributions of each
component of the proton’s motion ?
A: Linear
B: Helical
C: Circular
![Page 27: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/27.jpg)
Choice AIncorrect
This is the result if only the component of the motion along the magnetic field (x-component) is considered.
![Page 28: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/28.jpg)
Choice BCorrect
If you trace out a circle while moving down an axis, the resulting path is helical.
In this case, the proton’s motion along the field is at a constant velocity
![Page 29: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/29.jpg)
Choice CIncorrect
This is only the effect of the proton’s motion in the y-z plane.
![Page 30: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/30.jpg)
7. To find the radius of the projected motion of the proton in the y-z plane, choose all of the statements that are relevant.
(i) the magnetic force provides the centripetal acceleration
(ii) the magnetic force should be equated to the mass of the proton times centripetal acceleration
(iii) the centripetal acceleration is: where R is the radius of the circle
A: i & ii only
B: i & iii only
C: i, ii, and iii
€
a=v2
R
![Page 31: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/31.jpg)
Choice AIncorrect
This equation is the correct expression for centripetal acceleration and will be used to find the radius of the proton’s path.
€
a=v2
R
![Page 32: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/32.jpg)
Choice BIncorrect
As usual, we set F=ma. In this case the mass is the mass of a proton, and a is centripetal acceleration expressed as:
€
a=v2
R
![Page 33: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/33.jpg)
Choice CIncorrect
All of these statements are relevant to finding the radius of the proton’s path.
![Page 34: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/34.jpg)
8. Which of the following expressions is correct for the magnitude of the component of the
velocity perpendicular to the magnetic field?
A:
B:
C:
€
v=qBmR
€
v=qBRm
€
v=qBRsinθm
![Page 35: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/35.jpg)
Choice AIncorrect
Check your algebra
€
ma=Fmag
mv2
R=qvBsinθ
v =qBR sinθ
m
![Page 36: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/36.jpg)
Choice BIncorrect
Check your algebra
€
ma=Fmag
mv2
R=qvBsinθ
v =qBR sinθ
m
![Page 37: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/37.jpg)
Choice CCorrect
€
ma=Fmag
mv2
R=qvBsinθ
v =qBR sinθ
m
![Page 38: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/38.jpg)
9. Which of the following expressions is correct for the
period T?
A:
B:
C:
€
T =2πRm
qB
€
T =2πm
qBsinθ
€
T =qBsinθ2πm
![Page 39: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/39.jpg)
Choice ACorrect
Period:
€
T =2πR
v=
2πRmqBRsinθ
=2πm
qBsinθ
![Page 40: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/40.jpg)
Choice BIncorrect
Period:
€
T =2πR
v=
2πRmqBRsinθ
=2πm
qBsinθ
![Page 41: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/41.jpg)
Choice CIncorrect
Period:
€
T =2πR
v=
2πRmqBRsinθ
=2πm
qBsinθ
![Page 42: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/42.jpg)
10. Which one of the following expressions gives the pitch P of the helix (the distance
traveled in the x-direction during one revolution) ?
A:
B:
C:
€
P =vxT
€
P =vyT
€
P =vx
T
![Page 43: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/43.jpg)
Choice AIncorrect
The pitch of a helix is the distance traveled along the helical axis during one revolution. The helical axis is the x-axis in this case. We are not concerned with the y-component of motion here.
![Page 44: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/44.jpg)
Choice BIncorrect
The pitch of a helix is given by the following expression:
€
P =vxT
![Page 45: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/45.jpg)
Choice CCorrect
This is the correct expression for the pitch of the helix since the axis of the helix is the x-axis.
![Page 46: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/46.jpg)
11. Find the expression for the pitch of the helical path of the proton
described in the original problem.
Answer
![Page 47: A proton is shot with a velocity v at an angle to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.](https://reader035.fdocuments.us/reader035/viewer/2022062801/56649e505503460f94b476f3/html5/thumbnails/47.jpg)
€
vx =vcosθ
€
P =vcosθ2πmqBsinθ
=2πmv
qBcot θ
Since the x-component of the proton’s velocity is constant:
Since the x-component of the proton’s velocity is constant:
€
P =vxT =vcosθT
From question 9 we have:
From question 9 we have:
€
T =2πm
qBsinθ