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# Each of the electrons in a particle beam has a kinetic energy of $1.60 \times 10^{-17} \mathrm{J}$ . (a) What is the magnitude of the uniform electric field (pointing in the direction of the electrons' move-ment) that will stop these electrons in a distance of 10.0 $\mathrm{cm}$ ? (b) How long will it take to stop the electrons? (c) After the electrons stop, what will they do? Explain.

## a. b. $3.37 \times 10^{-8} \mathrm{s}$c. $1.76 \times 10^{14} \mathrm{m} / \mathrm{s}^{2}$

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##### Christina K.

Rutgers, The State University of New Jersey

LB
##### Aspen F.

University of Sheffield

##### Jared E.

University of Winnipeg

### Video Transcript

part of the problem. When an electron moves a distance off a Delta X in the direction off the electric field, the workmen will be called to the force times the distance. The Lexx force we have is, um, e turns electric field times Delta X Times course 1 80 This gives us minus e small e capitally Delta X. This is a walker. So the next world done will be equal to change. In kinetic energy, network is equipped to frantic energy final minus frantic energy Initial initial kind of energy. So the final time energy Here it is. Zero. This is you so evil. Recall to care E Divided by E. Delta X that is equal to 1.6 old time standing by minus 17 divided by 1.6 old times. Then the farmer minus 19 is the charge. Times the distance traveled is zero point in one's original meter. That is called the one time standard Forward tree. Uh, Newton Bakula, this is our elected field going to me. Um, the match you'd offer darling Force on the Electron is E. Smalley capitally and then from Newton's second Law, we can write acceleration Musical, too minus 50 The electric force divided by the Mass. Here we have electric force off E times skeptical. Lied about the mass and the tea we can find using Newton creation of motion That is a final velocity minus initially lost Theo I defy explanation. And so some student values here is a zero minus square root off to initial frantic energy divided by mass divided by minus lee. Right, But in this minus minus will cancel out. So we are left with their two times Pantic, two times mass Initial frantic energy divided by the times Capitally Then substituting your values, we get t really so square root off two times 9.11 is the mass times minus 31 times 1.6 old times dental apart minus 17 Position. Frantic energy divided by 1.6 old times. Tempting for a minus 19 is the charge times. The electric field we found is one doesn't power. Three defined issues us the time off 3.37 times 10 to the power minus state second, which is according to the three 0.7 nanoseconds Nazi. After being electron. After bringing the electron to rest, the electric force continues to act on it, causing the electron to accelerate in opposite direction to the electric field at the rate off exploration. Is it cool to e him for 1.6 time student ball minus 19 Dying's one for one time, standing on my tree, divided by 99.11 guy instead while minus 31 Katie, this gives us exploration A LL for 1.76 times 10 to the power seventies, 14 3 meters per second squared.

Wesleyan University
##### Christina K.

Rutgers, The State University of New Jersey

LB
##### Aspen F.

University of Sheffield

##### Jared E.

University of Winnipeg