What is the potential difference between two points in a uniform electric field?

[Genericcoder]

Hi guys I am learning about electrostatic on my own and was solving some problems but I am having problems with these questions please help.

An electron is released within a uniform electric field of a magnitude of 28,000 N/C generated by two parallel plates. The plates are separated by 4 cm. If the electron has moved across the entire gap between the plates, what is its speed?

We can get the force of the Particale in such electric field
which will be
F = 28 * 10^3 * - 1.6 * 10^-19;
F = -4.48 * 10^-15;

We know here it will follow a parabolic path so I have stopped from here I don't know where to start to solve this problem.

How much work is required to bring a 10.0 μC charge from infinity to 5.00 meters away from a point charge of -2.00 μC?

I solved this problem but can't find the answer on the given choices,since they don't provide answer here is how I tried to solve for it. I want to know if my answer is correct.

I reasoned through this as follows I assumed the charge is already 10 charge is 5 meters away,since the potential from infinity is zero and this would approximate result.
So I got the force that they were putting on each other distance 5 meters away as:

F = 9 * 10^9 * 10 * 10^-6 * -2 * 10^-6 / 5^2 = -7.2 * 10^-3;
So work done should be w = -7.2 * 10^-3 * 5 = -0.036J;
W = -3.6 * 10^-2

The answer exists in the multiple choice but I don't know if its correct please let me know if it is.


An electron moves 0.10 m along the direction of an electric field of a magnitude of 3.0 N/C. What is the potential difference between the electron’s initial and final points?

a. 4.8 x 10–20 V
b. 1.6 x 10–20 J
c. –4.8 x 10–20 J
d. –1.6 x 10–20 J

I don't know where to start to solve this problem.

Thanks for help in advance.

 

[BruceW]

We know here it will follow a parabolic path so I have stopped from here I don't know where to start to solve this problem.

I guess you could integrate the force over the path the electron takes, but there is a very useful property of conservative forces that you can use. Also, the question asks for the speed of the electron, so that implies to me that the electron was initially at rest. So in this case, the path of the electron becomes more simple anyway.

 

[BruceW]

I reasoned through this as follows I assumed the charge is already 10 charge is 5 meters away,since the potential from infinity is zero and this would approximate result.
So I got the force that they were putting on each other distance 5 meters away as:

F = 9 * 10^9 * 10 * 10^-6 * -2 * 10^-6 / 5^2 = -7.2 * 10^-3;
So work done should be w = -7.2 * 10^-3 * 5 = -0.036J;
W = -3.6 * 10^-2

The answer exists in the multiple choice but I don't know if its correct please let me know if it is.

I think you have got the right answer. But I think the way you calculated it and your reasoning are not right. You've used the force on the particle at 5 meters, and multiplied by 5 meters, but what would that actually mean? That the particle was being acted on by a constant force over 5 meters? The actual situation is that the particle is acted on by a varying force from infinity to the 5 meter point. I think it is just coincidence that you got the right answer. There's two possible ways to answer this question. One involves using the potential, and the other way involves integrating the force over the path. Are you familiar with these methods?

 

[BruceW]

An electron moves 0.10 m along the direction of an electric field of a magnitude of 3.0 N/C. What is the potential difference between the electron’s initial and final points?

a. 4.8 x 10–20 V
b. 1.6 x 10–20 J
c. –4.8 x 10–20 J
d. –1.6 x 10–20 J

I don't know where to start to solve this problem.

Thanks for help in advance.

What do you know about the electric potential and potential energy in electrostatics? They are two closely related but different things. One of the most important parts of electrostatics is learning how they relate to the electric field.

 

[Genericcoder]

Sorry for replying late was sleeping.
I am sometimes confused by electric potential sometimes in question. I know its is the work done or potential energy of a particle at specific place,and electric potential is work done per charge. For problem 2 I just used that U = Ufinal - UInititial; and since UInitial is approaching zero,so I neglected that.

For problem number 1 how could I think I solved it thanks for that hint BruceW I first we know since its conservative force then potential will transform to kinetic,so its potential is F * D,and also since we know its potential is positive coz it would want to go to the positive charge so we can change the sign in order to get the work done in order to put the electron in its current state.

W = 4.48 * 10^-15 * 4 = 1.792 * 10^-14;
1/2mV^2 = 1.729 * 10^-13;
1/2mV^2 = (4.48 * 10^-15 * 4);
V^2 = (2 * 1.792 * 10^-14) / (9.1 * 10^-31) ;
V = 1.98 * 10^7;For problem 3 we know that V = kQ / d and we derived that from integration I saw lecture of walter lewin on that. We also know that U / q = V,so we can do the following --> V = Vfinal - Vinitial , but I am still confused into how to think about this problem though I think I am over complicating it in my head..

 

[Genericcoder]

Sorry had to bump this coz it was going to page 2.

 

[BruceW]

I am sometimes confused by electric potential sometimes in question. I know its is the work done or potential energy of a particle at specific place,and electric potential is work done per charge.

You've said electric potential twice. So I think you meant to say electric potential energy in the first sentence. In this case, yes, you've understood it.

For problem 2 I just used that U = Ufinal - UInititial; and since UInitial is approaching zero,so I neglected that.

This is the correct way to do the problem. But your method to get Ufinal was not right. (Although you did get the right answer anyway).

...I think I solved it thanks for that hint BruceW I first we know since its conservative force then potential will transform to kinetic...W = 4.48 * 10^-15 * 4 = 1.792 * 10^-14;

You've got the right idea, but the calculation has a mistake. The plates are separated by 4 cm, so you should convert that into SI units before you use it in the equation, or it'll get complicated to keep track of the units.

For problem 3 we know that V = kQ / d and we derived that from integration I saw lecture of walter lewin on that. We also know that U / q = V,so we can do the following --> V = Vfinal - Vinitial , but I am still confused into how to think about this problem though I think I am over complicating it in my head..

You're given the electric field, so you need to relate that to the potential energy. The equation V = kQ / d is true for an electric field created by a point charge, but it is not true in this case, where they are telling us that the electric field is constant throughout space. In other words, you have a much simpler integration to do!

 

[Genericcoder]

I see since its constant electric field it should simplify to V = Ed; so we should have
The potential difference at point 0.1 to be
E = 3 * 0.1 = 0.3V but the answer isn't in the questions it would be in the choice if they asked potential energy Difference then it would be 0.3 * -1.6 * 10^-19 = -4.8 * 10^-20 that would be electric potential energy between the two points not electric potential. Did I miss something here ?

 

[BruceW]

The question was "What is the potential difference between the electron’s initial and final points?" And you've hit the nail on the head, the electric potential difference is 0.3V, but it is not one of the multiple-choice answers. And you've noticed that the electric potential energy difference is the same as one of the possible answers (answer c).

This is a very important skill for exams - trying to interpret the question, even when the question is worded badly. I think this is one of those situations, where the question wants the electric potential energy difference, but they only wrote 'potential difference'.

 

[Genericcoder]

Yes I agree one should always find patterns if the answer isn't included in the question.
One's assumption based on the given data would be right if the logic is correct :D.

Anyway thanks a lot for the help.

 

[BruceW]

glad to be of some help!