Find the magnitude of the magnetic field ∣∣B⃗ (r)∣∣ inside the cylindrical resistor, where r is the distance from the axis of the cylinder,

Question

Find the magnitude of the magnetic field ∣∣B⃗ (r)∣∣ inside the cylindrical resistor, where r is the distance from the axis of the cylinder, in terms of i, r, r0, l, and other given variables. You will also need π and μ0. Ignore fringing effects at the ends of the cylinder.

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RobertKer 6 months 2021-07-30T07:46:06+00:00 1 Answers 176 views 0

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    2021-07-30T07:47:43+00:00

    Answer:

    The magnetic field inside the cylindrical resistor is \dfrac{\mu_{0}ir}{2\pir_{0}^2}

    Explanation:

    Given that,

    Distance from the axis of the cylinder = r

    We need to calculate the magnetic field inside the cylindrical resistor

    Using formula of magnetic field

    \oint{\vec{B}\cdot\vec{dl}}=\mu_{0}i_{encl}

    B\cdot(2\pi r)=\mu_{0}\dfrac{i\pir^2}{\pi r_{0}^2}

    Where, r₀ = radius

    r = distance

    i = current

    |\vec{B}(r)|=\dfrac{\mu_{0}ir}{2\pir_{0}^2}

    Hence, The magnetic field inside the cylindrical resistor is \dfrac{\mu_{0}ir}{2\pir_{0}^2}

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