Orthogonal Fields Problem

Here is an interesting problem shared by Neeraj.

Let us make the following assumptions:
1) The electric field is along the $+ x$ axis
2) The magnetic flux density is along the $+ z$ axis
3) Gravity is along the $+ y$ axis

Let the particle\s initial velocity be $\vec{v} = (v_x, v_y, v_z)$, and let its charge be $q$ and its mass be $m$.

Computing the forces on the particle results in:

$F_x = q v_y B + q E = 0 \\ F_y = -q v_x B + m g = 0 \\ F_z = 0$

The first equation yields:

$v_y = - \frac{E}{B }$

So the velocity in the $y$ direction is initially negative. When the gravity becomes the only force remaining, it acts in the $+ y$ direction. So the speed of the particle diminishes as the velocity becomes less negative, before increasing again as the velocity becomes positive. The minimum speed in the $y$ direction is zero, and it reaches this value at:

$t_f = \frac{|v_y|}{g} = \frac{E}{B g }$

Note by Steven Chase
7 months, 1 week ago

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Sort by:

@LilDoug Greetings. This was an interesting one

- 7 months, 1 week ago

@Steven Chase Thanks

- 7 months, 1 week ago

@Steven Chase hey while writing $F_{x}$ , didn't it should be $qv_{y}B$??

- 7 months, 1 week ago

Good catch. I have corrected it

- 7 months, 1 week ago

@Steven Chase How can you reply me??

- 7 months, 1 week ago

What?

- 7 months, 1 week ago

@Steven Chase Try this 2 problems. Help me. Also thanks in advance. :)

- 7 months, 1 week ago

I would probably do these numerically

- 7 months, 1 week ago

- 7 months, 1 week ago

@Steven Chase sir I am giving you 1 page of my physics book

After that I will just ask the question through number.

- 7 months, 1 week ago

@Steven Chase Hello. Help me in 30th problem

- 7 months, 1 week ago

@Steven Chase Hello, Good Morning., help me. In 30th problem above.

- 7 months, 1 week ago

@Steven Chase You are replying Karan sir, but not me.
At least you should reply “ok Neeraj whenever I will get time, I will clear you doubt ”
At least you have to give one reply.
Now I am upset with you.

- 7 months, 1 week ago

Yeah, I'll look at it today. By the way, stop sending messages demanding that I reply to this or that. I don't owe you anything, and I will reply to whatever I want (or not reply).

- 7 months, 1 week ago

@Steven Chase what is the meaning of “ I don't owe you anything“
The sentence is grammatically incorrect.

- 7 months, 1 week ago

It's perfectly correct. It means that I do not owe you anything

- 7 months, 1 week ago

@Steven Chase Why you talk so rude?

- 7 months, 1 week ago

It's grammatically correct.

- 7 months, 1 week ago

@Krishna Karthik but what is it's meaning bro?
According to my research on internet- He wants to say I have not done anything to him, due to which he will repay me by telling solutions. Am I right?

- 7 months, 1 week ago

He means that it's his choice whether to help you or not. Of course; he's helping you out of his own volition. You aren't paying him to help you. So he doesn't owe you anything.

- 7 months, 1 week ago

@Krishna Karthik Exactly, but he is helping very much.
I don't think I will get another teacher like Steven sir. He is my favourite of all time

- 7 months, 1 week ago

Yeah; which is why you should be patient. Don't be relentless in doing classical mechanics. Keep reading; check brilliant sporadically, not all the time.

- 7 months, 1 week ago

@Krishna Karthik yeah bro, beside that no. 6 do you have Solved all 35 questions??

- 7 months, 1 week ago

I haven't got round to it yet. That's cause my schoolwork is ramping up right now. For you, however, IIT is schoolwork in itself. For me, because I'm not in Year 11 yet, this kind of work is not school work sadly😥

- 7 months, 1 week ago

@Krishna Karthik who said you to do school work. Don't do it. Simple.

- 7 months, 1 week ago

Lmao. If I don't do it, my grades will be horrible and I won't get into University for physics.

I'm kind of trying to figure out a balance between the both. Besides, my end of term holiday will approach soon. In my holiday, I will ditch boring schoolwork and work on physics more.

- 7 months, 1 week ago

@Krishna Karthik in which university you want to go? , Does they need your school work, I don't think so?

- 7 months, 1 week ago

@Krishna Karthik why you are denying me to solve classics mechanics relentlessly?

- 7 months, 1 week ago

I'm not denying you. I'm giving you a tip: When you have to wait for a response from Steven Chase, read a physics book. Try to learn new concepts rather than constantly solving problems.

Also, you should learn Linear Algebra. You are not very experienced in that. And you're a very fast learner. If you have any doubts, just ask me.

- 7 months, 1 week ago

@Krishna Karthik Thanks for your support.
By the way, what things did you have learnt in mathematics till now?

- 7 months, 1 week ago

@Steven Chase when do you usually wake up in morning?

- 7 months, 1 week ago

I have learned Linear Algebra, calculus up till Vector Calculus, Algebra, Trigonometry, Vectors.

- 7 months, 1 week ago

@Krishna Karthik Do you have learnt coordinate geometry, 3D Geometry?

- 7 months, 1 week ago

Yeah, of course. That stuff goes hand-in-hand with trig, algebra, and calculus. I'm mostly just learning maths for physics, really. But I want to have a really good mathematical foundation as an aspiring theoretical physicist.

To me though, the maths isn't really a struggle. I kind of get it naturally, like you guys.

- 7 months, 1 week ago

@Krishna Karthik I want to test you bro
I will give you 20 question of mathematics of the topics which you have learnt.
Will you give?
Whenever you will be free.

- 7 months, 1 week ago

Ok; sure. Give me the questions.

- 7 months, 1 week ago

@Krishna Karthik are you free now for 1 hour.?The test is of 1 hour.

- 7 months, 1 week ago

Yeah, sure. I'll do it in a few minutes. You can give me the questions now :)

- 7 months, 1 week ago

@Krishna Karthik You will not use desmos, Matlab, python, calculator. Or anything else. Only pen and page.
I am giving you problems right now Be ready for 1 hour.

- 7 months, 1 week ago

Sure. Cool bro. No graphing.

- 7 months, 1 week ago

Standard universities don't work that way. See; I'm not trying to get into IIT, obviously, because I'm an Australian citizen. I'm trying to get into a university such as Uni Melbourne for physics, and then work my way up to Caltech for Graduate.

- 7 months, 1 week ago

@Krishna Karthik If you go to Caltech, which course you want to pursue?,
I don't think there is any course with name physics?
There are some sub-topics.

- 7 months, 1 week ago

@Lil Doug Well, generally Theoretical Physics. Honestly, Caltech is the absolute best university to go into for Theoretical Physics (MIT is more engineering and mathematics focussed).

I want to go into Relativity (General and Special); Quantum Mechanics and Statistical physics, String Theory. Maybe I would also want to go into Rocket Science and Aerospace engineering. I don't really know.

- 7 months, 1 week ago