This is probably in the wrong section...

[Avengardh]

But I think we need a physics/math help thread, yeah, I do.

Only because I am in need of help right now.

So, without further ado, I am going to see if anyone here can help me figure this out (by this I mean more explain what is going on...I know I can get partial credit in the final because I wip up crap with math, but I want to understand what is happening), most likely, elementary problems/issues I have as of right now, since I am studying for my Physics II (calc-based) final and all of my classmates suck (as in, I think they are afraid/intimidated because I am a girl...and I turn E in the classroom...) so I can't ask them for help.

As of now, it is only one problem, because all the others I figured out, anyway, here it is:

1. A negative point charge q = -7.20 mC (milli-Coulombs, if I am correct) is moving in a reference frame. When the point charge is at the origin, the magnetic field it produces at the point x = 0.25 m, y=0, z=0, is B = (6.00 micro-Teslas)j and its speed is 800 m/s.
What are the x, y, and z components of the velocity V[initial] of the charge?

I was trying to figure that one out by reasoning from F = qv x B
But I still feel there is something I am missing...

At any rate, any help would be appreciated.

[Hypnos]

qvxB is the force on a charged particle in an ambient B field

There are couple of ways to solve the problem:

1. relativistically boost the 1/r^2 E-field from the particle's rest frame to the frame in question

2. Model the current as qv\delta(vt), then derive the B field from the potential sourced by that current

3. An approximation on #2 is to use the bio-savart law

[flan2dave]

Which way is the B field pointing? (that's the first "missing piece" of info that comes to mind)

[Avengardh]

qvxB is the force on a charged particle in an ambient B field

There are couple of ways to solve the problem:

1. relativistically boost the 1/r^2 E-field from the particle's rest frame to the frame in question

2. Model the current as qv\delta(vt), then derive the B field from the potential sourced by that current

3. An approximation on #2 is to use the bio-savart law
I think I am going with that one, dude, thanks.

[Avengardh]

Which way is the B field pointing? (that's the first "missing piece" of info that comes to mind)
Well, it's positive, and it's in the y-axis (j = y-axis) ^^.

[Hypnos]

Is it asking for the velocity of the charge (seems given -- 800 m/s)? Or the components of the magnetic field? Or is there more to the problem, like it started out somewhere else?

[Avengardh]

Is it asking for the velocity of the charge (seems given -- 800 m/s)? Or the components of the magnetic field? Or is there more to the problem, like it started out somewhere else? Nope, that is the whole problem.

Now that I look at your answers and I looked at Bio-Savart it looks odd to me...anyway, it is asking for the components of the initial velocity [v not] which is why I am a bit confused.

Edit: I really think it's just a simple vector thing....but I just don't know how to find it.

[Hypnos]

yeah, I'm confused too

The problem would make sense if they give a magnetic field vector at some location away from the instant location of the charged particle, asking you to find the velocity vector of the particle

[flan2dave]

The problem would make sense if they give a magnetic field vector at some location away from the instant location of the charged particle, asking you to find the velocity vector of the particle

Doesn't it though? When the particle moving at 800 m/s passes through the origin, a B field is created at .25, 0, 0 pointing in the positive y direction.

I think the particle is moving along the z-axis.

[Hypnos]

Doesn't it though? When the particle moving at 800 m/s passes through the origin, a B field is created at .25, 0, 0 pointing in the positive y direction.
I guess the problem is asking the components of this velocity, while giving you the magnitude -- I think that's weird

[Avengardh]

yeah, I'm confused too

The problem would make sense if they give a magnetic field vector at some location away from the instant location of the charged particle, asking you to find the velocity vector of the particle
Well, yes, the point charge is at the origin, and the B field it produces at the point <0.25m, 0, 0> is 6.0 micro-Teslas in the j direction. Does that make sense at all?

[flan2dave]

The magnitude of the B field will tell you how much to divvy the z and x components of the velocity.

[Avengardh]

I guess the problem is asking the components of this velocity, while giving you the magnitude -- I think that's weird
I just replied to you, haha, too late.

And yes, that is what is playing with my mind here, I got the problem wrong, but she only took away 2 points (20 problems, 50 points total), I can't totally read her hand-writing but she scribbled the answer: <607m/s i, 0 j, -521k>
I also thought it was going to end up in the z-axis....but, I don't really know where she got that answer.

[flan2dave]

Looks like I was right about the nature of the answer.

[Avengardh]

Looks like I was right about the nature of the answer.
Yes you were dude, but I still don't understand what goes with what...if that makes sense...

[Hypnos]

Oh, I see -- V_0 doesn't mean "initial speed," just the speed.

[Avengardh]

Oh, I see -- V_0 doesn't mean "initial speed," just the speed.
What? Oi....

Explain, please?

[Hypnos]

the problem gives the speed of the particle at the origin, but not the velocity.

it does give you the magnetic field at some fixed location away from the origin.

you are asked to compute the particle velocity given this information.

the biot-savart law should work

[flan2dave]

I normally see the biot-savart law done as an integration of a current. How could it be used for a moving point charge? *disregard question if it's apparent I'm being totally confused*

[Hypnos]

qv is like Idl

[Avengardh]

I normally see the biot-savart law done as an integration of a current. How could it be used for a moving point charge? *disregard question if it's apparent I'm being totally confused*
That was my exact question.

[Avengardh]

qv is like Idl
Now it makes sense.

[Avengardh]

Ok, wait, no it doesn't.

How am I supposed to solve for the vector when it's being crossed by r [vector, or the .25 m in the x direction]?

[flan2dave]

You can replace the cross with just sin A I think (solving for the angle will let you find the components you need).

I'm still stuck pondering about this..

[Hypnos]

B = qvxr/r^2

Since B has only has a y component, and r only has an x component, v can only have z or x components, by the properties of the cross product.

[Avengardh]

B = qvxr/r^2

Since B has only has a y component, and r only has an x component, v can only have z or x components, by the properties of the cross product.
Hmm, I know that, that is exactly what I have....what I am trying to understand now is how she solved for her answer, or in other terms, what do I multiply/cross to get: <607 m/s, 0 j, -512k> ?

Thanks though, both of you, at any rate.

[flan2dave]

I would try out some calculations to see what works, but I don't have my calc.

[Avengardh]

I would try out some calculations to see what works, but I don't have my calc.
I have, most of what I get is within the small range...hmm.

[Hypnos]

\mu_0/4\pi (-7.2e-3 C) (-512 m/s k ) x (0.25 m i)/(0.25 m)^3 = 6e-6 T j

you would've rearranged the above to solve for the (-512 m/s k)

To get the i component of v,

sqrt((800 m/s)^2-(-512 m/s)^2) = +/- 615 m/s

[Avengardh]

\mu_0/4\pi (-7.2e-3 C) (-512 m/s k ) x (0.25 m i)/(0.25 m)^3 [2?] = 6e-6 T i [j?]

you would've rearranged the above to solve for the (-512 m/s k)

To get the i component of v,

sqrt((800 m/s)^2-(-512 m/s)^2) = +/- 615 m/s
I thought the 6e-6 was a j and the 3 was a 2?
Ok, and I know this might sound dumb and redundant, but, my problem is just rearranging the equation, to me it looks as if the x for the cross product can't be broken....

[Hypnos]

I thought the 6e-6 was a j [...]
You're right -- I've corrected it.


[...] and the 3 was a 2?
The 3 is correct:

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/biosav.html


Ok, and I know this might sound dumb and redundant, but, my problem is just rearranging the equation, to me it looks as if the x for the cross product can't be broken....
Well, cross product has a partial inverse. Say you have vectors v = a i + b j + c k and r = f i + g j + h k. Then you have B = v x r = (bh - cg)i + (cf - ah)j + (ag - bf)k.

In this case, B has only the j component non-zero, (cf - ah). However, r has only the i component, so h = 0 -- this leaves only B_j = cf --> c = B_j/f.