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Current I(0) is flowing through a bent w...

Current `I_(0)` is flowing through a bent wire `atoctobtod` in `z-x` plane as shown in figure, then `ointvecB.vec(dl)` over the loop PQRS lying in the X-Y plane as shown in figure, due to the bent wire `acbd`

A

`(mu_(0)I_(0))/8`

B

`(mu_(0)I_(0))/7`

C

`(mu_(0)I_(0))/5`

D

`(mu_(0)I_(0))/3`

Text Solution

Verified by Experts

The correct Answer is:
D
`y=l/2 tan theta`
`dy=l/2sec^(2)theta d theta`
`8 int_(0)^((pi)/4) Bdycostheta+oint _(atobtoctod)vecB.vec(dl)=mu_(0)l_(0)`
`int_(0)^((pi)/2) (8mu_(0)I_(0))/(4pix). (2l/2)/(sqrt(x^(2)+(l^(2))/4)).l/2 sec^(2)theta cos theta+oint_(atobtoctod)vecB.vec(dl)=mu_(0)I_(0)`
`2/3 mu_(0)I_(0)+oint_(atobtoctod)vecB.dl=mu_(0)I_(0)`
`oint_(atobtoctod) vecB.vec(dl)=mu_(0)I_(0)-2/3mu_(0)I_(0)=(mu_(0)I_(0))/3`
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