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Calculation of magnetic field

  1. Dec 20, 2014 #1
    1. The problem statement, all variables and given/known data

    Consider a square whose successive sides of length [itex]L[/itex] has resistances [itex]R, 2R, 2R, R[/itex] respectively. If a potential difference [itex]V[/itex] is applied between the points (call them , say , A and B) where the sides with R and 2R meet. Find the magnetic field [itex]B[/itex] at the center of the square.

    2. Relevant equations
    [itex]R_s = R_1 + R_2 + R_3 + ... + R_n[/itex]
    [itex]\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... + \frac{1}{R_n}[/itex]
    [itex]V = iR[/itex]
    [itex]\oint \vec B \cdot d \vec s = \mu _0 i[/itex]

    3. The attempt at a solution
    The equivalent resistance of this combination is [itex]\frac{4R}{3}[/itex] . So, the current through [itex]R , 2R[/itex] are [itex] \frac{V}{2R} , \frac{V}{4R} [/itex] respectively. But, to calculate the magnetic field, what will be the amperian loop to imagine?
  2. jcsd
  3. Dec 20, 2014 #2


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    Does the magnetic field pattern have enough symmetry to use Ampere's law? If not, can you think of a different law that you can use?
  4. Dec 20, 2014 #3
    So, I should use Biot-Savart's law. But another question, can I use Biot-Savart's Law in case of variable electric field?
  5. Dec 20, 2014 #4


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    Last edited by a moderator: May 7, 2017
  6. Dec 20, 2014 #5


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