For a magnetic field strength of 2T, estimate the magnitude of the maximum force on a 1-mm-long segment of a single cylindrical nerve that h

Question

For a magnetic field strength of 2T, estimate the magnitude of the maximum force on a 1-mm-long segment of a single cylindrical nerve that has a diameter of 1.5mm.

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King 3 weeks 2021-08-25T02:36:41+00:00 1 Answers 0 views 0

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    2021-08-25T02:38:12+00:00

    Answer:

    Incomplete question

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    For a magnetic field strength of 2 T, estimate the magnitude of the maximum force on a 1-mm-long segment of a single cylindrical nerve that has a diameter of 1.5 mm. Assume that the entire nerve carries a current due to an applied voltage of 100 mV (that of a typical action potential). The resistivity of the nerve is 0.6ohms meter

    Explanation:

    Given the magnetic field

    B=2T

    Lenght of rod is 1mm

    L=1/1000=0.001m

    Diameter of rod=1.5mm

    d=1.5/1000=0.0015m

    Radius is given as

    r=d/2=0.0015/2

    r=0.00075m

    Area of the circle is πr²

    A=π×0.00075²

    A=1.77×10^-6m²

    Given that the voltage applied is 100mV

    V=0.1V

    Given that resistive is 0.6 Ωm

    We can calculate the resistance of the cylinder by using

    R= ρl/A

    R=0.6×0.001/1.77×10^-6

    R=339.4Ω

    Then the current can be calculated, using ohms law

    V=iR

    i=V/R

    i=0.1/339.4

    i=2.95×10^-4 A

    i=29.5 mA

    The force in a magnetic field of a wire is given as

    B=μoI/2πR

    Where

    μo is a constant and its value is

    μo=4π×10^-7 Tm/A

    Then,

    B=4π×10^-7×2.95×10^-4/(2π×0.00075)

    B=8.43×10^-8 T

    Then, the force is given as

    F=iLB

    Since B=2T

    F=iL(2B)

    F=2.95×10^-4×2×8.34×10^-8

    F=4.97×10^-11N

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