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A long straight conductor carrying curre...

A long straight conductor carrying current `I_1` is placed in the plane of a ribbon carrying current `I_2` parallel to the previous one. The width of the ribbon is b and the straight conductor is at a distance a from the near endge. Find the force of attraction between the two.

Text Solution

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Consider a thin strip at a distance x and of the thickness dx. It is
equilivalent to a long straight conductor carying `(I_2dx//b)` current.
`dF(foce of attraction)=(mu_0I_1)/(2pix)xx(I_2dx)/b=(mu_0I_1I_2)/(2pib)xx(dx)/x`
`:. F=(mu_0I_1I_2)/(2pib) int_a^(a+b)(dx)/x=(mu_0I_1I_2)/(2pib)In (a+b)/a`
This force is per unit length.
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