What determines the curvature of a particle's path in an electric field?

[nikoniko1234]

For this question, the ans is A, the ans said that the curvature of the path is determined by the acceleration of the particle.

There is two question I want to ask: 1. Why the curvature of the path is not determined by the force (electric force + weight) acting on the charge instead of it's acceleration?
2. Why option B is not correct? Since it's weight is increased so that the total downward force is increased.

 

[Orodruin]

The curvature is ultimately dependent on the relation between the acceleration and the velocity. The relation between the radius of curvature and these quantities is R = v^2/a. (Note that infinite radius of curvature corresponds to a straight line.) The force on the particle is related to its acceleration through Newton's second law.

The gravitational force is usually completely negligible on subatomic scales.

 

[nikoniko1234]

The curvature is ultimately dependent on the relation between the acceleration and the velocity. The relation between the radius of curvature and these quantities is R = v^2/a. (Note that infinite radius of curvature corresponds to a straight line.) The force on the particle is related to its acceleration through Newton's second law.

The gravitational force is usually completely negligible on subatomic scales.

Could you explain more please?Base on the options of the question.

 

[Qwertywerty]

The gravitational force is usually completely negligible on subatomic scales.

Sir , is that applicable here ?

And also ,
R = v²/a , so wouldn't increasing q or m decrease R ?

 

[Orodruin]

No, you need to provide some effort of working with the equations. For example, how do you obtain the dependence of the radius of curvature on the charge of the particle?

 

[Orodruin]

Sir , does that apply here ?

And also ,
R = v²/a , so wouldn't increasing q or m decrease R ?

If you had read my post properly, you would have seen that large R correspond to almost straight trajectories.

 

[Qwertywerty]

If you had read my post properly, you would have seen that large R correspond to almost straight trajectories.

So a higher velocity would mean a larger R right ?

 

[nikoniko1234]

If you had read my post properly, you would have seen that large R correspond to almost straight trajectories.

I think that the terms " increase the curvature of path" in this question means that the path of the particle become more close to the lower plate...

 

[Orodruin]

Which would happen for decreasing radius of curvature, which is what I was hinting at. Even if gravity is not negligible, the curvature would not increase with increasing mass (in fact, if q is non-zero, it would decrease). Can you see why? Hint: How does the movement of a mass in a gravitational field depend on the mass? Do objects with different masses fall with different acceleration?