Express your answer with the appropriate units.

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W

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Part B

If you release the electron from the position in A

$,$ what will be its kinetic energy when it is a distance $8\mathrm{.}001012$m

from the center of the lead nucleus? $($You can assume that the lead nucleus remains at rest, since it is much more massive than the electron.$)$

Express your answer with the appropriate units.

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K

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VP $23\mathrm{.}2\mathrm{.}2$

Part C

In a nuclear physics experiment, a proton $($mass $1\mathrm{.}671027$kg

$,$ charge $+$e$=+1\mathrm{.}601019$C

$)$ is fired directly at a target nucleus of unknown charge. $($You can treat both objects as point charges, and assume that the nucleus remains at rest.$)$ When it is far from its target, the proton has speed $2\mathrm{.}50106$m$/$s

$.$ The proton comes momentarily to rest at a distance $5\mathrm{.}291013$m

from the center of the target nucleus, then flies back in the direction from which it came. What is the electric potential energy of the proton and nucleus when they are $5\mathrm{.}291013$m

apart?

Express your answer with the appropriate units.

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Part D

What is the charge of the target nucleus?

Express your answer with the appropriate units.

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VP $23\mathrm{.}2\mathrm{.}3$

Part E

Two point charges are at fixed positions on the y

$-$axis: q$1=+$e

at y$=0$

and q$2=$e

at y$=$a

$.$ Find the work you must do to bring a third charge q$3=$e

from infinity to being at rest at y$=2$a

$.$

Express your answer in terms of the electric constant $0$

$,$ fundamental charge e

$,$ and variable a

$.$

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Part F

Find the total potential energy of the system of three charges.

Express your answer in terms of the electric constant $0$

$,$ fundamental charge e

$,$ and variable a

$.$

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VP $23\mathrm{.}2\mathrm{.}4$

Part G

A point charge q$1=+5\mathrm{.}00$nC

is at the fixed position x$=0$

$,$ y$=0$

$,$ z$=0$

$.$ You find that you must do $8\mathrm{.}10106$J

of work to bring a second point charge from infinity to the position x$=+4\mathrm{.}00$cm

$,$ y$=0$

$,$ z$=0$

$.$ What is the value of the second charge?

Express your answer with the appropriate units.

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q$2$

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Part H

Once the second charge is in place, how much additional work would you have to do to bring a third point charge q$3=+2\mathrm{.}00$nC

from infinity to the position x$=0$

$,$ y$=+3\mathrm{.}00$cm