What Is the Work Done by an External Force on a Transported Electron?

[victorializ]

Homework Statement

Point charges, Q1 = +56 nC and Q2 = -98 nC, are placed as shown. In Figure 18.1a, an external force transports an electron from point A to point B. The work done by the external force is closest to:
A) +620 eV
B) -920 eV
C) -620 eV
D) +920 eV
E) +770 eV

Homework Equations

v= kq/r
W= e (Vb-Va)

The Attempt at a Solution

i know I'm doing this completely wrong. i tried to get the electric potential at A from charge 1 & 2 and then added them. i did the same for the electric potential at point b from charge 1 & 2 . once i had the summed potentials i found the difference and then multiplied by the charge of an electron .

for A[(9 x 10^9) x (56 x 10^-9)/.6] + [(9x 10^ 9) x (-98 x 10^-9)/1 ] = -42 V

for B : [(9 x 10^9) x (56 x 10^-9)/1] + [(9x 10^ 9) x (-98 x 10^-9)/.6] =-966

Vb-Va = -924 V
-924 x (1.6 x 10 ^-19 ) = -1.47 x 10 ^ -16 eV which is nowhere close. i must be approaching this the wrong way.

 

[haruspex]

Your method seems fine. What do you get for the potential at B and for the work done?

 

[victorializ]

Your method seems fine. What do you get for the potential at B and for the work done?

i just edited and added the rest of my calculations in the original thread post! i must be doing something wrong .
the answer is supposed to be D) +920 eV

 

[dauto]

Your calculated energy is measured in Joules. You want it measure in eV's so that you can compare it with the possible choices. Hint: do not plug in the value of the constant e. Leave it symbolically as e.

EDIT: also keep in mind that the charge of the electron is -e, not e.

 

[victorializ]

Your calculated energy is measured in Joules. You want it measure in eV's so that you can compare it with the possible choices. Hint: do not plug in the value of the constant e. Leave it symbolically as e.

EDIT: also keep in mind that the charge of the electron is -e, not e.

so rather than multiplying it i would just leave my answer in joules but basically multiply by -1 because of -e which would leave me with about +920eV?

 

[dauto]

so rather than multiplying it i would just leave my answer in joules but basically multiply by -1 because of -e which would leave me with about +920eV?

Yes except that you're not leaving your answer in Joules. You're leaving it in eVs. I assume that was a typo.

 

[victorializ]

Yes except that you're not leaving your answer in Joules. You're leaving it in eVs. I assume that was a typo.

yes it was sorry haha. that makes sense thank you!

so why exactly don't you multiply it by the e constant?

 

[dauto]

yes it was sorry haha. that makes sense thank you!

so why exactly don't you multiply it by the e constant?

You do multiply by the e constant symbolically at the unit. The unit of volts "V" times the constant "e" equal the unit electron-volts. Symbolically you have
e * Volt = electron-volt or
e V = eV.

 

[victorializ]

You do multiply by the e constant symbolically at the unit. The unit of volts "V" times the constant "e" equal the unit electron-volts. Symbolically you have
e * Volt = electron-volt or
e V = eV.

oh wow okay that makes so much more sense ! thank you so much for all your help!