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# Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.

7. Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.

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The magnitude of magnetic field at a distance r from a long straight wire carrying current I is given by,

$|B|=\frac{\mu _{0}I}{2\pi r}$

In this case the magnetic field at a distance of 4.0 cm from wire B will be

$|B|=\frac{4\pi \times 10^{-7}\times 5}{2\pi\times 0.04}$             (I=5 A, r=4.0 cm)

$\\=2.5\times10^{-5} T$

The force on a straight wire of length l carrying current I in a uniform magnetic field B is given by

$F=BIlsin\theta$, where $\theta$ is the angle between the direction of flow of current and the magnetic field.

The force on a 10 cm section of wire A will be

$F=2.5\times10^{-5}\times8\times0.1 \times sin90^\circ$       (B=2.5 T, I=8 A, l = 10 cm, $\theta$=90o)

$F=2\times10^{-5} N$

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