Intro: It is five years in the future and you have a high paying job in the Deep

Question

Intro: It is five years in the future and you have a high paying job in the Deep Underground Science and Engineering Lab 4850 ft down inside a mine. Since you're making the big bucks you are asked to design a device to detect an important singly-charged positive ion (Q=1.6x10-19C) that has a mass of 2.18x10-26kg. You start by designing a velocity selector that will select ions that are traveling at 4x104m/s directed straight out of the page.

A. What must be the magnitudes of E and B in your veelocity selector so that particles traveling 4x104 m/s pass straight through? Remember, you are designing this -- pick values to make the velocity selector work.

B. You then send all the ions that are traveling 4x104 m/s out of the page into a deflection chamber that has a constant magnetic field of 0.0500T directed to the right. Where exactly (distance and direction) will the 2.18x10-26kg singly-charged (Q=1.6.10-19C) ions hit the screen in the deflection chamber (which is located on the inside wall of the chamber where the ions enter)?

Explanation / Answer

Part A)

It is common that the magnetic field in the velocity selector and the magnetic field in the deflection chamber be the same. Therefore I will choose a magentic field in the velocity selector as .05 T

From this, we can calculate a needed Electric Field to make the velcoity selector work

v = E/B

(4 X 104) = E/(.05)

E = 8 X 105 N/C

So those are the values that will work   E = 8.00 X 105 N/C and B = 0.0500 T

Part B)

The radius of the path of the charges is found by

r = mv/qB

r = (2.18 X 10-26)(4 X 104)/(1.6 X 10-19)(.05)

r = .109 m

The distance it hits the wall is the diameter of the travel, or twice the radius. Therefore it will hit at a distance of .218 m   or 21.8 cm

They also want to know which direction. By the right hand rule for the positive charge in a magnetic field, the charges will travel in a circular path and hit in a location above the entry point from the velocity selector.

So, in summary, 21.8 cm above the entry point.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

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