Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    3
    ReputationRep:


    The question is more about setting up the dynamical system than any of the Physics behind magnetic fields and stuff.

    I get  \mathbf{B} = (-x^2 + y^2 + 1, 2xy, 0)^T and so  \frac{d\mathbf{x}}{ds} \times \mathbf{B} = (0,0, B_yx_s - B_xy_s)^T where  B_x,B_y are the x,y components of  \mathbf{B}, and  x_s = \frac{dx}{ds} .

    Obviously from there I get that B_yx_s = B_xy_s . But from there I can't find anything that implies that  x_s = B_x, \; y_s = B_y.
    Attached Images
     
    Offline

    13
    ReputationRep:
    (Original post by TheFOMaster)


    The question is more about setting up the dynamical system than any of the Physics behind magnetic fields and stuff.

    I get  \mathbf{B} = (-x^2 + y^2 + 1, 2xy, 0)^T and so  \frac{d\mathbf{x}}{ds} \times \mathbf{B} = (0,0, B_yx_s - B_xy_s)^T where  B_x,B_y are the x,y components of  \mathbf{B}, and  x_s = \frac{dx}{ds} .

    Obviously from there I get that B_yx_s = B_xy_s . But from there I can't find anything that implies that  x_s = B_x, \; y_s = B_y.
    I think you're making it too complicated for yourself. By the formula for curl, you show that

     \displaystyle B_x = 1 + (y^2 - x^2)

    and

     \displaystyle B_y = 2 x y

    and that is pretty much it.  B_x, B_y are components of a vector "attached" at  (x, y) and integral curves of that vector field are precisely the field lines of B.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Are unpaid trial work shifts fair?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.