At what point on the x-axis is the magnetic field zero if the two currents are in the same direction?

Question

At what point on the x-axis is the magnetic field zero if the two currents are in the same direction?

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Khánh Gia 4 years 2021-08-03T12:04:48+00:00 1 Answers 26 views 0

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  1. niczorrrr
    0
    2021-08-03T12:05:53+00:00
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    Answer:

    0.67cm

    Explanation:

    We are given that

    Current ,I_1=5A

    I_2=2.5 A

    x_1=-2 cm

    x_2=2 cm

    d=x_2-x_1=2+2=4 cm

    Let x is the distance between two wires

    Magnetic field in the wire,B=\frac{2\mu_0I}{4\pi r}

    Where \frac{\mu_0}{4\pi}=10^{-7}

    r_1=x

    r_2=4-x

    B_1=B_2

    \frac{2\mu_0 I_1}{4\pi r_1}=\frac{2\mu_0I_2}{4\pi r_2}

    \frac{I_1}{r_1}=\frac{I_2}{r_2}

    \frac{5}{x}=\frac{2.5}{4-x}

    20-5x=2.5x

    20=2.5x+5x=7.5x

    x=\frac{20}{7.5}=2.67 cm

    Distance of 5A  wire from the point=-2+2.67=0.67 cm.

    Hence, at x=0.67 cm the magnetic field is zero.

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