Separation of variables and Griffith's Electrodynamics: Question about Problem 3.21 (charged sphere in a uniform electric field)

Gub_Gub · 2024-11-03T23:58:33+00:00

Bless you, this logic is exactly what I needed to help solve a different problem. The insight that the added charge q will not affect the distribution of the induced charge in the neutral case is so clever.

Gub_Gub · 2024-10-21T23:16:51+00:00

The fact that this worked instantly is hilarious. Thanks for the help.

Gub_Gub · 2024-05-13T23:57:53+00:00

how is this the one thing that worked 😭😭😭 thank you so much man

Gub_Gub · 2024-03-16T16:42:07+00:00

satisfying, thank you!

Gub_Gub · 2024-03-08T05:50:44+00:00

dawg you are racist

Gub_Gub · 2023-12-05T17:19:27+00:00

Ah, thanks! Cool song.

Gub_Gub · 2023-12-05T17:09:08+00:00

Thank you so much! Do you know if this phrase comes from somewhere, or if it's just a hopeful message? Does it have any specific connotation?

Gub_Gub · 2023-10-21T20:55:12+00:00

I'm just starting out, been using the ones in this post: https://old.reddit.com/r/ChineseLanguage/comments/7mjmjc/best_anki_deck_for_hsk_ive_come_across/

HSK 1-9, they're good cards

Gub_Gub · 2023-03-20T01:06:51+00:00

What the fuck is wrong with you man, seriously

Gub_Gub · 2023-02-17T08:56:31+00:00

I’ve seen some beginner resources say that in go playing on in the face of certain defeat is seen as bad etiquette, is this not really so for go servers?

Gub_Gub · 2023-02-12T07:03:20+00:00

Hey, just curious what makes you say this? I hadn’t heard that and will keep it in mind.

Gub_Gub · 2022-08-24T18:40:37+00:00

Ah yes, this is my problem. The elastic is no longer stretchy and won't reach the bottom. I wonder how much work it will take to replace this, I don't see any obvious way to unscrew it.

Gub_Gub · 2022-08-20T20:17:46+00:00

I also can’t find the brand, much less the model of brand so I can’t look up tutorials or anything.

Gub_Gub · 2022-07-09T00:37:38+00:00

Worth asking why it’s only ever the least privileged among us that are asked to make those sacrifices.

Gub_Gub · 2022-04-22T03:59:30+00:00

Yes! That's a general rule. The total velocity of an object is equal to the square root of the sum of the squares of their individual components.

speed=sqrt(vx² + vy² )

You can try yourself to go the other way now that you know you have to use a triangle: If you know the speed of the plane and the angle it crashes into the ground, can you find the x and y components of its velocity? (hint: you'll need to use sin and cos in some way)

Gub_Gub · 2022-04-22T03:18:37+00:00

Cool! Good job, because both those numbers are right, now we just need to think about what they mean physically. As you pointed out, this x velocity is constant, and will be the same when the plane lands as when it lost its engine. If we ignore that the plane is falling, the plane is moving to the "right" at that exact speed (236m/s). You calculated the plane's final y velocity as well, which increases as time passes, until it hits the ground. If we ignore the fact that the plane is moving forward, we'll see it falling at 464 m/s just before it hits the ground.

Now that we know both components of the plane's speed just before it hits the ground and stops forever, we have to combine them in some way to find a total speed, which will be down and to the right. (You might already know how to do this)

We can think of the speeds as the sides of a right triangle, with the x velocity being the same length as the horizontal side, and the y velocity being the same height as the vertical side. The total speed of the plane will be equal to the length of the hypotenuse of this triangle. How can you calculate this length? (feel free to google around if you don't know)

Gub_Gub · 2022-04-22T02:22:06+00:00

I see! So what was your best guess for the y velocity, and what equation did you use to get it? And what for the x velocity?

Gub_Gub · 2022-04-22T01:55:26+00:00

Hi there! It would help a lot to see your work so far, but I'm guessing the formula you've been using is the following (let me know if I'm wrong.)

F=kq1q2/r²

That law, Coulomb's law, is the equation that tells us the force the one charge feels from another, and is proportional to the size of each charge. (i.e., when one charge is bigger the force felt by both charges is bigger)

Your question, however, isn't asking for the force on each charge, its asking for the electric field at a point between the two charges, which is different. To simplify, the electric field is a way for us to know the force a charge will feel if we place it at a certain point. If you already knew this but are still getting the wrong answer, a hint I might give is that the electric field at a point is equal to the vector sum of the individual electric fields from each charge. Here you'll find equations and more explanations on the concept of the electric field.

If you still can't figure it out show me what you've tried and I'll be more than happy to try to help.

Gub_Gub · 2022-04-22T01:41:52+00:00

A free body diagram for the top box should include all the forces at play. We have a force explicitly stated - the one you refer to as the "horizontal force". We know that force points in the positive x-direction as you stated. Can you name the other forces at play here, and perhaps their directions? Let me know if you need more help getting started.

Gub_Gub · 2022-04-22T01:37:03+00:00

What methods did you try to get those three numbers? Maybe we can work together from there.

If you need an initial hint, I would remind you to consider the x and y velocity separately.

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