Magnetic Fields

[sugarbabee0]

Which of the following is NOT true of a magnetic field?

A. It can be generated by a moving charge.

B. It can accelerate a moving charge.

C. It can exert a force on a moving charge.

D. It can increase the speed of a moving charge.


Answer is D. What is the difference between B and D?
The explanation says "Since the magnetic force FB on a charged particle q is always perpendicular to the velocity v of the particle—because FB = q(v ×B)—the force FB can do no work on q. Therefore, by the work–energy theorem, W = DKE, FB cannot change the kinetic energy (or, therefore, the speed) of q. Thus, statement D is false."

Any help please? I don't get it. Thanks

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[Brahms2010]

If you apply a force in a specific direction, it may increase the speed of an object in that direction. But with magnetic fields, the force has no component in the direction of particle movement (completely perpendicular). This means the particle can move in an orbit but the distance from the epicenter will not change. Remember velocity is defined by a speed and direction so only one of these characteristics need to change to affect velocity.

 

[sugarbabee0]

If you apply a force in a specific direction, it may increase the speed of an object in that direction. But with magnetic fields, the force has no component in the direction of particle movement (completely perpendicular). This means the particle can move in an orbit but the distance from the epicenter will not change. Remember velocity is defined by a speed and direction so only one of these characteristics need to change to affect velocity.

Thanks for the quick reply. So I now understand that the speed does not change. Then how does the charge accelerate? Is it the velocity (direction part ; not speed) that is changing? And if so, what direction does than change with respect to everything else?

 

[fizzgig]

as it turns a charge in a circle centripetal acceleration changes direction and velocity changes direction, even though speed does not change

 

[sugarbabee0]

as it turns a charge in a circle centripetal acceleration changes direction and velocity changes direction, even though speed does not change

I don't think we are dealing with centripetal acceleration here. Are we? Doesn't mention anything about circle or spheres or anything round.

 

[fizzgig]

sorry maybe i am being confusing (or confused... both happen daily).

if you whirl a ball around on a string, you have centripetal force towards the center, there's centripetal acceleration even if the ball speed doesnt change, because the acceleration applied changes the ball direction with each timestep vs changing the speed. the tension in the string only pulls perpendicularly to the ball's current velocity, and since there is no component of acceleration directly opposite the velocity tangent vector that you draw, that is why there is no speed change.

ok, in this case you ALSO have a force that is acting only perpendicularly to the velocity, which causes the charge to turn a little at every time step, and at each new timestep you draw, the force continues to ONLY act perpendicularly, and so yes you do end up with an orbit as brahms pointed out.

without a drawing it's kind of obnoxious but remember F = v x B, cross product. only the portion of the velocity that is perpendicular to B is acted on, and the force itself is perpendicular to both.

draw a typical 3d coordinate set of axes. velocity points right, B points out. vxB yields F pointing down in that instant. this perpendicular force, like the string pulling on the ball only perpendicularly, changes the direction of the velocity vector. v points right and a bit down now. all of v is still perpendicular to B, and F now points down and a little left. the whole coordinate axes get rotated CW around the B vector axis... this continues and you trace out a circle.

someone let me know if i'm off.

 

[sugarbabee0]

sorry maybe i am being confusing (or confused... both happen daily).

if you whirl a ball around on a string, you have centripetal force towards the center, there's centripetal acceleration even if the ball speed doesnt change, because the acceleration applied changes the ball direction with each timestep vs changing the speed. the tension in the string only pulls perpendicularly to the ball's current velocity, and since there is no component of acceleration directly opposite the velocity tangent vector that you draw, that is why there is no speed change.

ok, in this case you ALSO have a force that is acting only perpendicularly to the velocity, which causes the charge to turn a little at every time step, and at each new timestep you draw, the force continues to ONLY act perpendicularly, and so yes you do end up with an orbit as brahms pointed out.

without a drawing it's kind of obnoxious but remember F = v x B, cross product. only the portion of the velocity that is perpendicular to B is acted on, and the force itself is perpendicular to both.

draw a typical 3d coordinate set of axes. velocity points right, B points out. vxB yields F pointing down in that instant. this perpendicular force, like the string pulling on the ball only perpendicularly, changes the direction of the velocity vector. v points right and a bit down now. all of v is still perpendicular to B, and F now points down and a little left. the whole coordinate axes get rotated CW around the B vector axis... this continues and you trace out a circle.

someone let me know if i'm off.

Oooo I see. I think my problem is that I've always thought of a Magnetic Field as a Field or plain; whereas it seems more like a cylindrical pole as you're describing it. And the charge is free to move on its own and therefore it orbits the magnetic field and doesn't get closer (towards the magnetic field).

The example you have about the ball/string and centripetal acc helped a lot. So in that case, the pole holding the string would be like the magnetic field right?

If my understanding is wrong, please let me know.
Thanks

 

[fizzgig]

there are vectors describing direction ('poles') but it's not just 1 pole = a Bfield.

it can be drawn as a set of lines going from N to S. the simplest picture is where the lines are all straight. if you take a whole bunch of needles and push them through a rectangle of styrofoam and then stick the ends into a second rectangle of styrofoam, it looks like that. there are infinitely many lines that can describe what direction the field is going, and in this case they all go parallel. this is roughly what it looks like i believe on the inside of a MRI bore, all lines of the Bfield run parallel down the bore.

if you just have one little N-S magnet you've seen the lines drawn for that - they are not parallel anymore but they are still nonintersecting.

in both cases these are lines of potential just like in an electric field - they tell you how strong the field is along that line - in this case the magnetic field strength vs electric or gravitational or whatever.

ok so if a particle enters a field that looks like this (x means Bfield points into screen) and a positive particle flies into it
x x x x x
x x x x x
x x x x x <----o

you can see there are many 'poles' that are the coordinate axes i was talking about. the Bfield is constant here, so ANYWHERE that particle enters or wherever it goes once it's there, there is a Bfield line that can be drawn that will be the coordinate axis for the cross product, and that Bvector along that axis points the same direction with the same magnitude as every other Bfield line.

so the particle flies in perpendicular to B. when it hits, it sees B(intoscreen) and its velocity is v(totheleft). crossproduct is B*v*sin90 = Bv, and direction of the force is by the right hand rule. because the force is directly upward, having no acceleration IN or OPPOSITE the direction of the particle's current velocity, it will not speed it up or slow it down. the acceleration is perpendicular to the particle velocity and forces its trajectory to point slightly less left and slightly more up (magnitude constant). at this next tiny timestep, the exact same thing happens.

i know its weird to think of this 'orbit' without a single center for it to be swinging around, but no matter WHERE the velocity points in the plane i drew it in, B x v is going to make a force perpendicular to it. every time v changes direction so does the force on the particle. there is no single center here as with the ball on the string, because the field is a big steady field vs a point creating the field. but similarly, if you have the same force magnitude always pressing/pulling a particle perpendicularly, you get a circle traced out.

so how is the radius determined? by the strength of the force, which determines how much the velocity's current direction is going to be changed. and the force will be bigger if the particle is moving faster or if the Bfield is stronger.

probably longer than i meant, but see how that sits with you.

 

[sugarbabee0]

ok so if a particle enters a field that looks like this (x means Bfield points into screen) and a positive particle flies into it
x x x x x
x x x x x
x x x x x <----o

you can see there are many 'poles' that are the coordinate axes i was talking about. the Bfield is constant here, so ANYWHERE that particle enters or wherever it goes once it's there, there is a Bfield line that can be drawn that will be the coordinate axis for the cross product, and that Bvector along that axis points the same direction with the same magnitude as every other Bfield line.

so the particle flies in perpendicular to B. when it hits, it sees B(intoscreen) and its velocity is v(totheleft). crossproduct is B*v*sin90 = Bv, and direction of the force is by the right hand rule. because the force is directly upward, having no acceleration IN or OPPOSITE the direction of the particle's current velocity, it will not speed it up or slow it down. the acceleration is perpendicular to the particle velocity and forces its trajectory to point slightly less left and slightly more up (magnitude constant). at this next tiny timestep, the exact same thing happens.

Thank you. I really understand this much better now (I hope I do at least). So the charge basically 'orbits' above the B (not coming closer or further away from it) and this is only due to the perpendicular (to both v and B) 'centripetal' force. Thats how the acc is changing but the speed is constant.

If its a +q charge in the B and v you explained, wouldn't the force be pushing it down (counterclockwise 'orbit')?


And just to differentiate b/w this case (a moving in a magnetic field) and a moving charge creating a B, please tell me if the following makes sense: A moving charge creates a magnetic field circling its path. For example, if a + charge or current is traveling up a vertical wire, the magnetic field (if viewed from on top of the wire) is counterclockwise. Is that correct?

Thanks for all the help btw!!!

 

[Rabolisk]

Yes, the magnetic field is counterclockwise from the top view.

 

[fizzgig]

sonofa....

yes, sugarbabee. not only can i not tell right from left, i had the formula wrong.

F= qv x B not qB x v

and that is how you get questions wrong lol. order matters.

you are correct: the way i drew my picture, since the cross prod is qv x B, a positive test charge will deflect DOWN, not up as i wrote. good call.

and yes to your second observation too. if you're looking down and positive current runs towards you, point your right thumb towards you (in direction of I) and wrap your fingers around the 'wire'. Bfield made will be CCwise.

 

[sugarbabee0]

Thank you fizzgig!!! If I get any B question right on the MCAT it'll be only b/c of you! Now I've got to figure out how to do better on my verbal

Thanks again tho