# Velocity of an electron within a weak electric field?

This is the question:

"An electron is released from rest in a weak electric field given by vector E = -1.80 10-10 N/C jhat. After the electron has traveled a vertical distance of 1.2 µm, what is its speed? (Do not neglect the gravitational force on the electron.)"

So far, the only approach I can think of is by using the equation Δy= 1/2 a*t. Since a = (e*E)/m and t = Δx / v(not), I have:

Δy = 1.2 µm = (.5) * [ (1.6E-19 C * -1.8E-10 N/C) / 9.11E-31 kg ] * (Δx / v)^2.

Since I have two unknowns (the Δx and v), I have been stuck for a while now. If anyone could offer any insight it would be greatly appreciated. This problem has been driving me mad!! Thanks in advance for any efforts or hints!

Dick
Homework Helper
You can't use (delta x)/v=(delta t) unless the motion has uniform velocity. Not true here. You can either use F=ma to analyze the motion or you can use conservation of energy to do it more easily.

Dick,

Maybe I'm missing something here but I don't see it, what do you mean by using the conservation of energy? Are you suggesting that I should use the kinetic form, by setting mgh = 1/2 mv^2? If so I don't understand why the Electric field charge could be involved at all. Please explain a little bit further as I am not the brightest of physics students. Thank you.

tiny-tim
Homework Helper
welcome to pf!

hi islimst3ri! welcome to pf!

(try using the X2 icon just above the Reply box )
… what do you mean by using the conservation of energy? Are you suggesting that I should use the kinetic form, by setting mgh = 1/2 mv^2? If so I don't understand why the Electric field charge could be involved at all.

all fields supply energy

the energy is the work done by the field: force "dot" displacement

for gravity, it's mgh (force mg, displacement h)

for electric fields, it's qEh (force qE, displacement h)

so use the work energy theorem … change in KE = work done by the fields

so use the work energy theorem … change in KE = work done by the fields

When I follow this approach, I have get
W = KE = qEh
= (1.6E-19 C)(-1.8E-10 N/C)(1.2E-6 m)
= -3.46E-35 J

After finding work, I plugged it into W = 1/2 mv2 as follows:

-3.46E-35 J = (.5)(9.1E-31 kg)(v2)
-6.91E-35 J = (9.1E-31 kg)(v2)
-7.60E-5 J/kg = (v2)

Since you cannot take a square-root of a negative number, I am once again stuck staring at this problem. Is there something that I'm missing or did wrong on the steps above? Thank you guys for being patient with me.

tiny-tim
Homework Helper
what happened to gravity?

(and don't forget electrons are negative)

Tim,

So WebAssign is down right now thus I can't check my answer. But I'll show my work and could you please scan over it to see if its right. A simple yes or no will suffice.

WE-Field = KE = qEh
= -(1.6E-19 C)(-1.8E-10 N/C)(1.2E-6 m)
= 3.46E-35 J

Wgravity = mgh
= (9.1E-31 kg)(9.81 m/s2)(1.2E-6 m)
= 1.07E-35 J

Using W = 1/2 mv2 for both E-field and gravitational field, I got v = .00872 and .00485 m/s, respectively. I then subtracted one from the other and get .00386 m/s, or 3.86 mm/s (the units WebAssign was looking for). How does this look?

gneill
Mentor
Is the electron rising or falling in the electric field? The gravitational field?

Since the electric field is moving with the vector in the direction of j-hat, it is moving upwards, while the gravitational field, intuitively, is moving downward. Since the electron was able to travel vertically for 1.2 µm, this indicates that the E-field is stronger than the g-field, thus this was why I subtracted the g-field speed from the e-field speed to get the electron's speed. However, I submitted this and still got the wrong answer. What am I doing wrong?

gneill
Mentor
Since the electric field is moving with the vector in the direction of j-hat, it is moving upwards, while the gravitational field, intuitively, is moving downward. Since the electron was able to travel vertically for 1.2 µm, this indicates that the E-field is stronger than the g-field, thus this was why I subtracted the g-field speed from the e-field speed to get the electron's speed. However, I submitted this and still got the wrong answer. What am I doing wrong?

Start by making clear what your coordinate system is. Assign directions to $$(\hat{i},\hat{j},\hat{k})$$. What does the negative sign mean for the E field magnitude? What sign should you assign to g if it's a vector?

u r making mistakes in the signs
otherwise the method looks quite fine to me....