Motion of a charged particle in an electric field

In summary, the given conversation discusses the acceleration of different nuclei through the same potential difference and determines which one completes the acceleration with the lowest speed and which one has the greatest momentum. Using the equations F=ma=QE and mv∝QE, the experts determined that the answer for the lowest speed is 1H1 and the answer for the greatest momentum is α1H1.
  • #1
Nemo's
69
0

Homework Statement



Each of the nuclei below are accelerated from rest through the same potential difference.Which one completes the acceleration with the lowest speed?
1H1 4He2 7Li3
9Be4

Homework Equations



F=ma=QE

The Attempt at a Solution


v∝a∝Q/m so for lowest v Q/m lowest is 1 so answer is 1H1

Homework Statement



The following particles are each accelerated from rest through the same potential difference. Which one completes acceleration with the greatest momentum?
α β proron neutron

Homework Equations


F=ma=QE



The Attempt at a Solution


mv∝QE so biggest mass and biggest charge give biggest momentum so the answer is α
 
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  • #2
1H1 has the largest Q/m.
While a larger Q/m leads to a larger velocity, those are not proportional to each other.

mv∝QE is not true.
 
Last edited:
  • #3
The energy gained by each particle = q x V
They all pass through the same V so the energy gained for each in order is 1, 2, 3 and 4 units.
This is KE so for each use 0.5mv^2 with the appropriate masses to find the values of velocity, v.
 
  • #4
mfb said:
1H1 has the largest Q/m.
Yes that's right I don't know why I reversed it. My bad. So it must be the Lithium.

While a larger Q/m leads to a larger velocity, those are not proportional to each other. mv∝QE is not true.
Why's that?
 
  • #5
technician said:
The energy gained by each particle = q x V
They all pass through the same V so the energy gained for each in order is 1, 2, 3 and 4 units.
This is KE so for each use 0.5mv^2 with the appropriate masses to find the values of velocity, v.
Thank you so much the energy approach is a lot
easier
 
  • #6
Nemo's said:
Why's that?
Why should the equation be true?
Energy and momentum are not the same.
 
  • #7
O.K so force (EQ) is directly proportional to the rate of change of momentum(Δmv/t) This one is true right?
 
  • #8
##F=\frac{dp}{dt} = m \frac{dv}{dt} = ma## (for constant m), indeed. As time is not given, I don't think this helps here.
 
  • #9
I see. So using proportionality here can't solve this problem.
O.K so by using the energy method I can get the speed of each particle then I could multiply each speed by the corresponding mass to get the momentum?
The problem is it's a multiple choice question and I shouldn't be wasting so much time on a single question in an exam. Isn't there a faster way ?
 
  • #10
O.K so by using the energy method I can get the speed of each particle then I could multiply each speed by the corresponding mass to get the momentum?
You can do this, or just compare the different particles ("larger mass leads to whatever, that leads to ..., ...")
 
  • #11
The charge of the particles is1, 2, 3 4...so the energy gained is also 1, 2 3 and 4 (relatively!)
The mass of the particles is 1, 4, 7 and 9.
so using energy =1/2 m v2 gives
1 = 1/2 x 1 x v2
2 = 1/2 x 4 x v2
3 = 1/2 x 7 x v2
4 = 1/2 x 9 x v2

if you sort this out you should see that for 1 v2 = 2
for 2 v2 = 1
for 3 v2 = 6/7
for 4 v2 = 8/9
 
  • #12
O.K Thank you so much :D
 

1. What is the relationship between the motion of a charged particle and an electric field?

The motion of a charged particle is influenced by the presence of an electric field. The particle will experience a force in the direction of the electric field, causing it to accelerate in that direction.

2. How does the direction of the electric field affect the motion of a charged particle?

The direction of the electric field determines the direction of the force experienced by the charged particle. If the electric field and the particle have opposite charges, the force will be in the direction of the electric field. If they have the same charge, the force will be in the opposite direction.

3. What factors affect the acceleration of a charged particle in an electric field?

The acceleration of a charged particle in an electric field is affected by the strength of the electric field, the charge of the particle, and the mass of the particle. A stronger electric field, a higher charge, and a lower mass will result in a greater acceleration.

4. How does the velocity of a charged particle change in an electric field?

The velocity of a charged particle changes as it accelerates in the direction of the electric field. As the particle moves, it may also experience a change in direction if the electric field changes direction or if the particle's acceleration causes it to curve.

5. What is the equation for calculating the force on a charged particle in an electric field?

The force on a charged particle in an electric field can be calculated using the equation F=qE, where F is the force, q is the charge of the particle, and E is the strength of the electric field.

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