Velocity of an electron within a weak electric field?

[islimst3ri]

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]

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.

 

[islimst3ri]

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]

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

 

[islimst3ri]

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]

what happened to gravity?

(and don't forget electrons are negative)

 

[islimst3ri]

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.

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

W_gravity = 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]

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

 

[islimst3ri]

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]

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?

 

[NEILS BOHR]

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