39:06 The magnetic field 0.02 m from a wire is 0.1 T. What is the magnitude of the magnetic field 0.01 m from the same wire?

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39:06
The magnetic field 0.02 m from a wire is 0.1 T. What is the magnitude of the magnetic field 0.01 m from the same wire?

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Tài Đức 5 months 2021-08-13T01:33:34+00:00 1 Answers 0 views 0

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    2021-08-13T01:34:45+00:00

    Answer:

    The magnetic field 0.01m from the wire is 0.2T.

    Explanation:

    The magnetic field B at a distance R due to a wire carrying current I is

    B = \dfrac{\mu_o I}{2\pi R}.

    Now, let us call B_1 the magnetic field at R_1 and B_2 the magnetic field at R_2:

    B_1 = \dfrac{\mu_o I}{2\pi R_1},

    B_2 = \dfrac{\mu_o I}{2\pi R_2}.

    Dividing B_1 by B_2 we get

    \dfrac{B_1}{B_2} = \dfrac{\dfrac{\mu_o I}{2\pi R_1} }{\dfrac{\mu_o I}{2\pi R_2} }

    \dfrac{B_1}{B_2} = \dfrac{\mu_o I}{2\pi R_1}* \dfrac{2\pi R_2}{\mu_oI}.

    \dfrac{B_1}{B_2} = \dfrac{2\pi R_2}{2\pi R_1}

    \boxed{\dfrac{B_1}{B_2} = \dfrac{R_2}{R_1}}

    Now we put in the numbers

    B_1 = 0.1T,\: \:  R_1 = 0.02m and R_2 = 0.01m to get:

    \dfrac{0.1T}{B_2} = \dfrac{0.01m}{0.02m}

    \dfrac{0.1T}{B_2} = 0.5

    solving for B_2 we get:

    B_2 = \dfrac{0.1T}{0.5}

    \boxed{B_2 = 0.2T}

    which is the magnetic field at 0.01 meters from the wire.

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