EK Physics #863 AC current question

[slz1900]

---

Members don't see this ad.

There are two charged plates and a point charge in between them. The distance between the plates is 20 m, the mass of the charge is 1 kg, the charge is 2 C, and the object reaches a max velocity of 20 m/s. What's the maximum voltage between the plates?

a) 25 V
b) 50 V
c) 100 V
d) 200 V



My answer: C
Answer: d

I used conservation of energy:

qV = 1/2 mv^2

However, the explanation says that you have to use:

V = v^2dm/(2qx) where d is 20 m and x is 10 m. Why doesn't the equation I used work? Isn't electrical potential all converted into kinetic energy?

Also, I suspect that the answer for 864 is a typo. If you have the book can you confirm?

 

[milski]

There are two charged plates and a point charge in between them. The distance between the plates is 20 m, the mass of the charge is 1 kg, the charge is 2 C, and the object reaches a max velocity of 20 m/s. What's the maximum voltage between the plates?

a) 25 V
b) 50 V
c) 100 V
d) 200 V



My answer: C
Answer: d

I used conservation of energy:

qV = 1/2 mv^2

However, the explanation says that you have to use:

V = v^2dm/(2qx) where d is 20 m and x is 10 m. Why doesn't the equation I used work? Isn't electrical potential all converted into kinetic energy?

Also, I suspect that the answer for 864 is a typo. If you have the book can you confirm?

The charge starts in between the plates - it seems that the implication is that the charge is in the middle between the plates. Since the field between the plates is uniform, only half of the full potential (that's where 10/20 comes from) is available to it. With your formula you have calculated that half of the potential between the plates is 100 V, so the full potential is 200 V.

 

[slz1900]

The charge starts in between the plates - it seems that the implication is that the charge is in the middle between the plates. Since the field between the plates is uniform, only half of the full potential (that's where 10/20 comes from) is available to it. With your formula you have calculated that half of the potential between the plates is 100 V, so the full potential is 200 V.

Hmm, I don't think it starts in between the plates. It's part of a passage and another question says that it starts "almost touching one of the plates".

Regardless, wouldn't max PE be given by qV and max KE be given by 1/2 mv^2? I don't get why distances are relevant since they give you the velocity.

 

[milski]

Hmm, I don't think it starts in between the plates. It's part of a passage and another questions says that it starts "almost touching one of the plates".

No idea then. 😕 Do they have any further explanation? The formula that they use is essentially what you are using, with the 10/20 coefficient thrown in it. I don't see where else the 10 m can come from - either the particle is moving from the middle to a plate or from a plate to the middle. 😕

 

[slz1900]

No idea then. 😕 Do they have any further explanation? The formula that they use is essentially what you are using, with the 10/20 coefficient thrown in it. I don't see where else the 10 m can come from - either the particle is moving from the middle to a plate or from a plate to the middle. 😕

The explanation says that max velocity is reached halfway between the plates and acceleration is constant. They derive that equation from v^2 = 2ax, V=Ed, and F=qE.

I think I get it actually. Since it reaches its max velocity in between the two plates, you are actually calculating Ed/2 for voltage, and when you use qV = KE you are actually calculating qEd/2 = KE, so your calculated voltage is actually the voltage required to speed it up to 20 m/s at the END of the plates, but because it reaches its max velocity in the middle, you have to use more voltage. Pretty much what you said

 

[milski]

What happens in the middle? If they've said at some point in the passage that that's where the max speed is reached, it will makes sense, but without outside intervention, the charge should continue to accelerate towards the other plate.

 

[slz1900]

What happens in the middle? If they've said at some point in the passage that that's where the max speed is reached, it will makes sense, but without outside intervention, the charge should continue to accelerate towards the other plate.

It gives you a piecewise graph of the voltage vs time that shows it alternates between the plates.