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    Magnetic Field Generated by a Short Current

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    Calculate magnetic field generated by a short current carrying segment of wire for the spot indicated in the diagram below.

    . (0.5m, 0.5m)

    (0,0)_____________>__________________ (1m, 0)

    I= 2A
    |---------------- 1m -----------------------|

    © BrainMass Inc. brainmass.com December 24, 2021, 8:37 pm ad1c9bdddf
    https://brainmass.com/physics/biot-savart-law/magnetic-field-generated-short-current-294255

    SOLUTION This solution is FREE courtesy of BrainMass!

    According to Biot-Savart law the magnetic field due to a current carrying segment is given by:
    (1.1)

    In our case we can write:
    (1.2)
    The directionality of the cross product is determined by the right hand rule and in this case the magnetic field points out of the page.
    However:
    (1.3)
    And
    (1.4)
    Thus, equation (1.1) now becomes:
    (1.5)

    All that is left is to integrate between :
    (1.6)
    To solve the integral we use:

    Therefore, equation (1.6) becomes:
    (1.7)
    The integrand is an even function, so we can use:
    (1.8)

    This is a simple integration, and we will use the fact that:

    (1.9)
    Back to equation (1.8) we obtain:

    (1.10)

    Note that when we let we regain the field for infinite wire:

    What is left is to plug in the numbers:

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 8:37 pm ad1c9bdddf>
    https://brainmass.com/physics/biot-savart-law/magnetic-field-generated-short-current-294255

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