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Aditi Agrawal posted an Question
June 27, 2020 • 15:46 pm 30 points
  • IIT JAM
  • Physics (PH)

Please solve this question...

Problem 1.14 Suppose that f is a function of two variables (y and z) only. Show that the gradient Vf = (af/0y)ý +(0f/8z)2 transforms as a vector un- der rotations, Eq. 1.29. [Hint: (af/8y) = (8f/8y)(8y/8y) + (0f/az)(8z/0y), and the analogous formula for df/8z. We know that y= y cos o+ z sin ộ and Z=-y sino+zcos p; "solve" these equations for y and z (as functions of y and Z), and compute the needed derivatives 3y/8y, 3z/0y, ctc.]

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  • comment-profile-img>
    Ghost.

    Statement of Question- del(f) is a vector quantity so you have to prove it transform in a similar manners as a normal vector when axis are rotated by certain angle. i.e if del(f) is really a vector quantity so it must have to follow transformation rule of a normal vector. Regards

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    got ur point

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    thanks

  • comment-profile-img>
    Ghost.

    here i have attached the file, you can write the transformation into matrix form as well and operate on components of function.

    cropped1606407907.jpg
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    thank you very much

  • comment-profile-img>
    Ruby negi best-answer

    see ....

    cropped751611214.jpg
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    also please explain that what does question says

    eduncle-logo-app

    ques says that u have to prove the gradient del F transforms like rotation of coordinate axis y and z...

    eduncle-logo-app

    ok thank you very much..it helped me a lot

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    always welcome.

  • comment-profile-img>
    Ruby negi Best Answer

    see this solution.. for any help do let me know...

    cropped1037121909.jpg
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    how does thus ybar and z bar came.. can you please provide its derivation

    eduncle-logo-app

    y bar and z bar is given in the question...

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    and if you want to derive it. u can rotate y, z along x - direction.

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    I am attaching. wait.

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    ok

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