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:

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

#ElectricityAndMagnetism

Easy Math Editor

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Comments

@LilDoug Greetings. This was an interesting one

Steven Chase - 9 months, 2 weeks ago

@Steven Chase Thanks

Talulah Riley - 9 months, 2 weeks ago

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

Talulah Riley - 9 months, 2 weeks ago

Good catch. I have corrected it

Steven Chase - 9 months, 2 weeks ago

@Steven Chase How can you reply me??

Talulah Riley - 9 months, 2 weeks ago

@Talulah Riley – What?

Steven Chase - 9 months, 2 weeks ago

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

Talulah Riley - 9 months, 2 weeks ago

I would probably do these numerically

Steven Chase - 9 months, 2 weeks ago

@Steven Chase No, please

Talulah Riley - 9 months, 2 weeks ago

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

After that I will just ask the question through number.

Talulah Riley - 9 months, 2 weeks ago

@Steven Chase Hello. Help me in 30th problem
Thanks in advance.

Talulah Riley - 9 months, 2 weeks ago

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

Talulah Riley - 9 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.

Talulah Riley - 9 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).

Steven Chase - 9 months, 1 week ago

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

Talulah Riley - 9 months, 1 week ago

@Talulah Riley – It's perfectly correct. It means that I do not owe you anything

Steven Chase - 9 months, 1 week ago

@Steven Chase – @Steven Chase Why you talk so rude?

Talulah Riley - 9 months, 1 week ago

@Talulah Riley – It's grammatically correct.

Krishna Karthik - 9 months, 1 week ago

@Krishna Karthik – @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?

Talulah Riley - 9 months, 1 week ago

@Talulah Riley – 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.

Krishna Karthik - 9 months, 1 week ago

@Krishna Karthik – @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

Talulah Riley - 9 months, 1 week ago

@Talulah Riley – 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.

Krishna Karthik - 9 months, 1 week ago

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

Talulah Riley - 9 months, 1 week ago

@Talulah Riley – 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😥

Krishna Karthik - 9 months, 1 week ago

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

Talulah Riley - 9 months, 1 week ago

@Talulah Riley – 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.

Krishna Karthik - 9 months, 1 week ago

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

Talulah Riley - 9 months, 1 week ago

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

Talulah Riley - 9 months, 1 week ago

@Talulah Riley – 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.

Krishna Karthik - 9 months, 1 week ago

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

Talulah Riley - 9 months, 1 week ago

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

Talulah Riley - 9 months, 1 week ago

@Lil Doug

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

Krishna Karthik - 9 months, 1 week ago

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

Talulah Riley - 9 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.

Krishna Karthik - 9 months, 1 week ago

@Krishna Karthik – @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.

Talulah Riley - 9 months, 1 week ago

@Talulah Riley – Ok; sure. Give me the questions.

Krishna Karthik - 9 months, 1 week ago

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

Talulah Riley - 9 months, 1 week ago

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

Krishna Karthik - 9 months, 1 week ago

@Krishna Karthik – @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.

Talulah Riley - 9 months, 1 week ago

@Talulah Riley – Sure. Cool bro. No graphing.

Krishna Karthik - 9 months, 1 week ago

@Lil Doug

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.

Your admission into a university depends upon your IB score and your school grades (I'm in an IB school).

Krishna Karthik - 9 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.

Talulah Riley - 9 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.

Krishna Karthik - 9 months, 1 week ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$