Electric Field Homework: Rank Protons by Acceleration

[Philip KP]

Homework Statement

The figure below shows five protons that are launched in a uniform electric field E (green). The magnitude and direction of the launch velocities are indicated. Rank the protons according to the magnitude of their accelerations due to the field, greatest first. Justify.

https://canvas.ewu.edu/courses/1017106/files/35335813/preview

Homework Equations

E=k(Q/r^2)
–e = –1.60 * 10–19 C.
E=F/Q
F=k((Qxq)/(r^2))
F=ma

The Attempt at a Solution

Well I know that the charge of proton is the positive value of the charge of electron. I also feel like I know which equations are needed, but I'm not sure about if for instance proton d is moving at 5m/s after it is going against the electric field? That means the acceleration must be pretty great to go against the uniform electric field. I'm not sure, I feel lost and can't meet with teacher until after its due. Any help appreciated

 

[Philip KP]

Not sure how to allow the image to be seen so I attached pdf

 

[gneill]

Not sure how to allow the image to be seen so I attached pdf

Hi Philip KP. Welcome to Physics Forums.

You can upload various formats of image files such as jpeg or giff and insert them as full images in the body of your post (see the options next to the individual image icon associated with the attached file).

For your posted problem, what determines the magnitude of the acceleration of a charge in an electric field? Does the formula depend on velocity?

 

[berkeman]

Homework Statement

The figure below shows five protons that are launched in a uniform electric field E (green). The magnitude and direction of the launch velocities are indicated. Rank the protons according to the magnitude of their accelerations due to the field, greatest first. Justify.

https://canvas.ewu.edu/courses/1017106/files/35335813/preview

Homework Equations

E=k(Q/r^2)
–e = –1.60 * 10–19 C.
E=F/Q
F=k((Qxq)/(r^2))
F=ma

The Attempt at a Solution

Well I know that the charge of proton is the positive value of the charge of electron. I also feel like I know which equations are needed, but I'm not sure about if for instance proton d is moving at 5m/s after it is going against the electric field? That means the acceleration must be pretty great to go against the uniform electric field. I'm not sure, I feel lost and can't meet with teacher until after its due. Any help appreciated

Welcome to the PF.

Hmm, that's a pretty confusing question (at least for me). The acceleration in a uniform E field is independent of any initial velocity. It just depends on the magnitude and direction of the E-field, and the charge and mass of the object.

You've correctly re-stated the problem, so I'm not sure what they are really asking. The velocities will certainly be different as the protons are accelerated by the field, but their accelerations will be the same. Maybe try answering the question about ranking their velocities, and see if that might be what they are asking. Can you submit your answer electronically to see if it's right? How many tries do you have?

EDIT -- beaten out by gneill again!

 

[Philip KP]

It's not electronic unfortunately. Good old fashion paper turn in. I guess I do know the mass of protons though is 1.67x10^-27 kg. I also understand the strength of the electric field depends on how close it is to the charge.

 

[berkeman]

I also understand the strength of the electric field depends on how close it is to the charge.

No, the field that the protons are launched into is specified as a uniform electric field. The field from each of the protons depends on the distance from the proton, but that doesn't enter into the force calculation for the force on the protons due to the uniform electric field that they are launched into.

 

[Philip KP]

No, the field that the protons are launched into is specified as a uniform electric field. The field from each of the protons depends on the distance from the proton, but that doesn't enter into the force calculation for the force on the protons due to the uniform electric field that they are launched into.

Ok so the equations involving "r" (distance) are irrelevant

 

[Philip KP]

Ok so the equations involving "r" (distance) are irrelevant

Would kinetic energy come into play here? Since we know the velocity and mass of protons?
KE=(1/2)mv^2

 

[berkeman]

Ok so the equations involving "r" (distance) are irrelevant

In this case, yes. If the E-field were not uniform, and were caused by some charge somewhere, then the distance r would be important.

You can get a uniform E-field between the plates of a capacitor, for example.

I still don't know what this problem could be asking, though. Unless they want you to rank the velocities instead of accelerations. I suppose it could be a trick question -- the answer is that all of the protons experience the same acceleration in the uniform E-field, and then say what happens to the vector velocities and rank them instead...?

 

[berkeman]

Would kinetic energy come into play here? Since we know the velocity and mass of protons?
KE=(1/2)mv^2

Maybe. Certainly you could rank the KEs as a function of time, but that doesn't seem to be what they are asking for...

 

[Philip KP]

In this case, yes. If the E-field were not uniform, and were caused by some charge somewhere, then the distance r would be important.

You can get a uniform E-field between the plates of a capacitor, for example.

I still don't know what this problem could be asking, though. Unless they want you to rank the velocities instead of accelerations. I suppose it could be a trick question -- the answer is that all of the protons experience the same acceleration in the uniform E-field, and then say what happens to the vector velocities and rank them instead...?

Ugh yeah my professor likes to give more conceptual questions sometimes so there might not be hard calculations to do but instead just a rule or law I need to be explaining

 

[berkeman]

Ugh yeah my professor likes to give more conceptual questions sometimes so there might not be hard calculations to do but instead just a rule or law I need to be explaining

So it might indeed be a trick question. Since you are handing in the paper version, you could say "they all have the same acceleration in the uniform E-field" and explain why. Then rank their velocities versus time just in case that's what they meant to ask...

 

[Philip KP]

So it might indeed be a trick question. Since you are handing in the paper version, you could say "they all have the same acceleration in the uniform E-field" and explain why. Then rank their velocities versus time just in case that's what they meant to ask...

So uniform electric field causes their acceleration to be the same...even if they have same mass and moving at different velocities?

 

[berkeman]

So uniform electric field causes their acceleration to be the same...even if they have same mass and moving at different velocities?

You tell me... What is the equation for the force on a charged particle in a uniform electric field E, related to the particle's charge and its mass...

 

[berkeman]

And what is the related equation for the acceleration of the particle in that situation...

 

[Philip KP]

You tell me... What is the equation for the force on a charged particle in a uniform electric field E, related to the particle's charge and its mass...

I'm trying to find where it talks about uniform electric fields in my book but they are don't have anything saying "uniform". But I think the equation for force on a charge is F=Q x E
And the only equation I can think of for acceleration and force is F=ma

 

[berkeman]

I'm trying to find where it talks about uniform electric fields in my book but they are don't have anything saying "uniform". But I think the equation for force on a charge is F=Q x E

Yes. And so what would the resulting acceleration be?

 

[Philip KP]

Yes. And so what would the resulting acceleration be?

F=ma=Q x E?
m(same for all protons) x a(what we need to find) = [ Q(which is same for all protons) x E (which is uniform)]

So we need to find the force

 

[Philip KP]

So I cheated a bit and googled how to find acceleration from velocity of proton and got this on Yahoo
F = Qvb
(Q- charge of proton = 1.6 x 10 ^-19 C (constant))
(v- velocity of proton) We know their velocities
(b-magnetic field) We know the E is uniform

F=ma We find force from equation above
(Electromagnetic force acting on proton)
(m- mass of proton = 1.67 x an^-27 kg (constant))
(a - acceleration of proton) We need to find this

combine the two formulas:
a = Qvb/m

I don't know if magnetic field is same as electric field

 

[Philip KP]

F=ma=Q x E?
m(same for all protons) x a(what we need to find) = [ Q(which is same for all protons) x E (which is uniform)]

So we need to find the force

Since F=Q x E but E is uniform does that mean F=Q??

 

[berkeman]

b-magnetic field

There is no magnetic B field specified in this problem...

 

[berkeman]

m(same for all protons) x a(what we need to find) = [ Q(which is same for all protons) x E (which is uniform)]

This looks correct to me.

 

[gneill]

Since F=Q x E but E is uniform does that mean F=Q??

"uniform" means that it is constant in magnitude and direction everywhere (or at least over the region of interest). You can't drop a term from an equation just because it's constant; at the very least it will "break" the units. A force (Newtons) is not the same as a charge (Coulombs), just as a force is not an acceleration; the "m" is required in the equation F = m⋅a, otherwise you don't have an equation.

 

[Philip KP]

There is no magnetic B field specified in this problem...

Ok so magnetic field and electric field aren't same

 

[Philip KP]

This looks correct to me.

How do I find the acceleration then, I'm missing the force

 

[gneill]

How do I find the acceleration then, I'm missing the force

You don't need to find a particular value for the force. You just need to find an expression for it, and note what values it depends on, and whether or not any of them differ from case to another in your problem.

 

[Philip KP]

You don't need to find a particular value for the force. You just need to find an expression for it, and note what values it depends on, and whether or not any of them differ from case to another in your problem.

What differs in the problem is their distance maybe, their velocities and their direction. Other than that I assume their acceleration since that's what we are looking for.

 

[gneill]

What differs in the problem is their distance maybe, their velocities and their direction. Other than that I assume their acceleration since that's what we are looking for.

That's why you need to write an expression for the acceleration, so you can test your assumptions.

 

[Philip KP]

That's why you need to write an expression for the acceleration, so you can test your assumptions.

So like Acceleration,=? meters/s^2 Q=1.6x10^-19 C, m=1.67x10^-27kg, E=? N/C, F=? Newtons,
a=F/m
F= QxE
a=(QxE)/m
Only problem is there is nothing about direction or velocity

 

[gneill]

So like Acceleration,=? meters/s^2 Q=1.6x10^-19 C, m=1.67x10^-27kg, E=? N/C, F=? Newtons,
a=F/m
F= QxE
a=(QxE)/m
Only problem is there is nothing about direction or velocity

That's not a problem, it's a bonus and a clear result! You now now that the acceleration does not depend upon direction or speed or distance; It only depends on the charge, the mass, and the electric field. So what can you conclude for the different cases presented?

 

[Philip KP]

That's not a problem, it's a bonus and a clear result! You now now that the acceleration does not depend upon direction or speed or distance; It only depends on the charge, the mass, and the electric field. So what can you conclude for the different cases presented?

Their accelerations are the same?? That just doesn't seem like him. (professor)

 

[gneill]

Their accelerations are the same?? That just doesn't seem like him. (professor)

Yes, the accelerations are all identical. It is the correct result for the question in the form it was given.

The question may seem like a trick, or perhaps it is incorrect due to a typo or otherwise, yet even so it got you to think about the physics of the situation.

 

[Philip KP]

Ok thanks gneill and berkeman. I guess you guys had said their accelerations were same in the beginning but it definitely helped figuring out why. I''ll talk to my professor tomorrow and I think it's actually due Tuesday so if there's something I'm missing I'll bring it up tomorrow?

Thanks!

 

[gneill]

Ok thanks gneill and berkeman. I guess you guys had said their accelerations were same in the beginning but it definitely helped figuring out why. I''ll talk to my professor tomorrow and I think it's actually due Tuesday so if there's something I'm missing I'll bring it up tomorrow?

That would be fine!

Thanks!

You're very welcome.