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A condutor carrying current I is placed ...

A condutor carrying current I is placed parallel to a current per unit width `j_(0)` and width d, as shown in the Find the force per unit length on the conductor
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Text Solution

Verified by Experts

The correct Answer is:
`(mu_(0)ij_(0))/(pi) tan^(-1) ((d)/(2h))(-hatk)`
`F=2 intdF sin 0`
` =2 int (mu_(0))/(4pi) (2j_(0)dx.i)/(h^(2) +x^(2)) . Sintheta`
`=(mu_(0))/(pi) j_(0) ih int(dx)/sqrt(h^(2) +x^(2)) (h)/sqrt(h^(2) +x^(2))`
`=(mu_(0))/(pi) j_(0)i.hunderset(0)overset(d//2)int(dx)/((h^(2) + x^(2))`
`= (mu_(0))/(pi) j_(0)ih[(1)/(h) tan^(-1)' (x)/(h)]_(0)^(d//2)`
`oversetrarrF = (mu_(0)j_(0)i)/(pi) tan^(-1)' (d)/(2h) (-hatk)`

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