electricity capacitors

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So drawn above is a parallel plate capacitor separated by a distance "d" .
A proton (mass m) is placed on top of the positively charged plate. The charge on the capacitor is Q and the capacitance is C. If the E-field in the region between the plates has a magnitude of E, which of the following expressions gives the time required for the proton to move up the other plate?

A. d√(eQ/mC)
B. d√(m/eQC)
C. d√(2eQ/mC)
D. d√(2mC/eQ)

answer: D this might be a good mcat question?...

cloak25, there have been 123 views and no answer--which main equations does the explanation say to use?

Ignoring equations for a moment:
- higher mass will make the particle move slower and take more time -> mass has to be in the enumerator
- higher capacitance would imply a higher dielectric constant, harder for the particle to move -> capacitance has to be in the denominator.
done.

You can also play around with the units but that's a bit trickier and requires you to remember more things.

Originally Posted by milski

Ignoring equations for a moment:
- higher mass will make the particle move slower and take more time -> mass has to be in the enumerator
- higher capacitance would imply a higher dielectric constant, harder for the particle to move -> capacitance has to be in the denominator.
done.

You can also play around with the units but that's a bit trickier and requires you to remember more things.

milski you're brilliant. I'm going to keep that mind---I never thought of determining the answer by using the physical relationships...lol--i'm a bit slow

Why does a higher dielectric constant mean that particle has a harder time moving?

Originally Posted by milski

Ignoring equations for a moment:
- higher mass will make the particle move slower and take more time -> mass has to be in the enumerator
- higher capacitance would imply a higher dielectric constant, harder for the particle to move -> capacitance has to be in the denominator.
done.

You can also play around with the units but that's a bit trickier and requires you to remember more things.

i figured as much, but can you think of a way to use equations? i got t = (2dm/qE)^0.5..i can't think of a way to keep d outside the square root.

i was using d = vo*t + 1/2 at^2 and F=qE

Originally Posted by chiddler

i figured as much, but can you think of a way to use equations? i got t = (2dm/qE)^0.5..i can't think of a way to keep d outside the square root.

i was using d = vo*t + 1/2 at^2 and F=qE

I did it like this..

C=Q/V, then V=Q/C

If we want to find the velocity in order to determine the time we probably want to use kinetic energy, which we can get from potential energy. U=kqq/r so V=U/q since the potential energy is going to have turned into KE, then we have V=mv^2/2q

mv^2/2q = Q/C (q=e)
v^2 = 2eQ/mC
v= sqrt 2eQ/mC

since v=d/t --> t=d/v

then we get
t= d*sqrt mc/2eQ

I just don't get why my 2 is on the denominator and not in the numerator like the answer choice..

ty.

tried to do that initially

i couldn't think how to relate distance to that >.>

On the phone, so rather brief:

Find the final velocity when the particle reaches the other plate from energy conservation (potential turning into kinetic)

Keeping in mind that the motion is with uniform acceleration, the average speed will be half of the final speed.

Calculate time based in distance and average speed.

I have not tried this but it should work.

explanation says to find acceleration first. once you find acceleration, you can use y=1/2at^2 to find time.

F=ma
a = F/m
a = qE/m = eE/m.
E=V/d and V=Q/C
so, a = eQ/mdC. substituting eQ/mdC for acceleration into d=1/2at^2

answer D.

this is how you solve it using equations, obviously but I just wanted to see if anyone can explain it using physical relationships to gain a better understanding conceptually. milski came the closest though

Originally Posted by cloak25

explanation says to find acceleration first. once you find acceleration, you can use y=1/2at^2 to find time.

F=ma
a = F/m
a = qE/m = eE/m.
E=V/d and V=Q/C
so, a = eQ/mdC. substituting eQ/mdC for acceleration into d=1/2at^2

answer D.

this is how you solve it using equations, obviously but I just wanted to see if anyone can explain it using physical relationships to gain a better understanding conceptually. milski came the closest though

that's what i did but is incorrect because this solution makes d into a square root. none of the answer choices reflect that.

Originally Posted by SaintJude

Why does a higher dielectric constant mean that particle has a harder time moving?

Found answer to my question:

"At first, it is easy to push charge on to the capacitor, as there is no charge there to repel it. As the charge stored increases, there is more repulsion and it is harder (more work must be done) to push the next lot of charge on." -IOP

Originally Posted by pm1

I did it like this..

C=Q/V, then V=Q/C

If we want to find the velocity in order to determine the time we probably want to use kinetic energy, which we can get from potential energy. U=kqq/r so V=U/q since the potential energy is going to have turned into KE, then we have V=mv^2/2q

mv^2/2q = Q/C (q=e)
v^2 = 2eQ/mC
v= sqrt 2eQ/mC

since v=d/t --> t=d/v

then we get
t= d*sqrt mc/2eQ

I just don't get why my 2 is on the denominator and not in the numerator like the answer choice..

What you have found is the final velocity - remember, it's a uniformly accelerating motion. The average velocity is half of that and the time will be twice what you've found, which will bring the 2 in the top part under the square root.

Both energy and kinetics solutions work.
pm1 already did the energy solution, the only correction there is the switch from final velocity to average velocity.
cloak25 has the correct kinetics solution. chiddler, there are two d-s multiplied under the square root, one comes from t=sqrt(2d/a), the other comes from a=eQ/mdC. That gives you a d in front of the radical.

thanks a very good correction.

Given: q,d,Q,C,E

d = 1/2 at^2
t^2 = 2d/a

F= m/a
F = eE (E = d/V) (Q = CV) (E = Q/dC) so
F = eQ/dC = ma

a = eQ/dCm

t^2 = 2d/a
t^2 = 2Cmd^2 /eQ

take square root of both sides and.......
t = d√(2mC/eQ)

Originally Posted by milski

Ignoring equations for a moment:
- higher mass will make the particle move slower and take more time -> mass has to be in the enumerator
- higher capacitance would imply a higher dielectric constant, harder for the particle to move -> capacitance has to be in the denominator.
done.

You can also play around with the units but that's a bit trickier and requires you to remember more things.

Your brilliance shall echo through the ages.