- #1
Electro n00b
- 2
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1.Homework Statement
BACKGROUND:
A positive helium ion He+ (mass 6.7 x 10-27 kg, charge 2e) is released from rest from the surface of a +1000 V electrode, as shown in the diagram below. It crosses (in vacuum) the gap between the electrodes, passes through a small hole in a 0 V electrode and into a magnetic field, and then begins to move in a curved path as shown. The magnetic field is uniform in the hatched region to the right of the 0 V electrode and is zero to the left of the 0 V electrode (Note: the lines do not indicate the direction of the magnetic field). The electrodes are circular disks with radius r = 2.0 cm and are separated by a distance d = 2.0 mm. The magnetic-field strength is 1.0 T. Picture attached of magnetic field and electrodes.
QUESTIONS:
(i) What is the direction of the magnetic field? Sketch the trajectory that the ion executes while it is within the magnetic field, and explain why the trajectory takes this shape.
(ii) Calculate the speed with which the ion enters the magnetic field, and use this to determine whether the ion can exit the magnetic field without colliding with the 0 V electrode.
(iii) Explain qualitatively how your answer to (ii) would change if the potential difference across the electrodes were increased.
2. Homework Equations
Part i)right hand rule?
Part ii) qU = 1/2 mv^2 , U being the voltage
3. The Attempt at a Solution
For part i) When I use the right hand rule on this question I get that the magnetic field would be coming out of the page but I'm not overly confident that I am correct. The trajectory would be looping back on the 0V electrode in a counter clockwise direction.
Part ii) I used the qU = 1/2 mv^2 formula to get v = √((2qU)/m), which gave me 7.73 x 10^14 m/s
I'm not sure what equation to use to figure out if the ion can exit the magnetic field without colliding with the 0V electrode.
Part iii) As voltage is increase the velocity would increase due to voltage being on the numerator of the rearranged equation for part ii)
BACKGROUND:
A positive helium ion He+ (mass 6.7 x 10-27 kg, charge 2e) is released from rest from the surface of a +1000 V electrode, as shown in the diagram below. It crosses (in vacuum) the gap between the electrodes, passes through a small hole in a 0 V electrode and into a magnetic field, and then begins to move in a curved path as shown. The magnetic field is uniform in the hatched region to the right of the 0 V electrode and is zero to the left of the 0 V electrode (Note: the lines do not indicate the direction of the magnetic field). The electrodes are circular disks with radius r = 2.0 cm and are separated by a distance d = 2.0 mm. The magnetic-field strength is 1.0 T. Picture attached of magnetic field and electrodes.
QUESTIONS:
(i) What is the direction of the magnetic field? Sketch the trajectory that the ion executes while it is within the magnetic field, and explain why the trajectory takes this shape.
(ii) Calculate the speed with which the ion enters the magnetic field, and use this to determine whether the ion can exit the magnetic field without colliding with the 0 V electrode.
(iii) Explain qualitatively how your answer to (ii) would change if the potential difference across the electrodes were increased.
2. Homework Equations
Part i)right hand rule?
Part ii) qU = 1/2 mv^2 , U being the voltage
3. The Attempt at a Solution
For part i) When I use the right hand rule on this question I get that the magnetic field would be coming out of the page but I'm not overly confident that I am correct. The trajectory would be looping back on the 0V electrode in a counter clockwise direction.
Part ii) I used the qU = 1/2 mv^2 formula to get v = √((2qU)/m), which gave me 7.73 x 10^14 m/s
I'm not sure what equation to use to figure out if the ion can exit the magnetic field without colliding with the 0V electrode.
Part iii) As voltage is increase the velocity would increase due to voltage being on the numerator of the rearranged equation for part ii)