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Numericals · Q12

Q.Currents of equal magnitude flow through two long parallel wires having a separation of 1.35 cm. If the force per unit length on each of the wires is 4.76×10−24.76\times10^{-2} N, what must be I?

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For two long parallel wires carrying equal current II, separated by distance dd, the force per unit length is FL=μ0I22πd\dfrac{F}{L}=\dfrac{\mu_0 I^2}{2\pi d} (Section 10.11, with I1=I2=II_1=I_2=I). Solving for II: I=FL⋅2πdμ0I=\sqrt{\dfrac{F}{L}\cdot\dfrac{2\pi d}{\mu_0}}. Substituting F/L=4.76×10−2F/L=4.76\times10^{-2} N/m, d=1.35 cm=0.0135d=1.35\ \text{cm}=0.0135 m, μ0=4π×10−7\mu_0=4\pi\times10^{-7} …

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