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A current carrying loop consists of 3 id...

A current carrying loop consists of 3 identical quarter circles of radius R, lying in the positive quadrants of the x-y, y-z and z-x planes with their centres at the origin, joined together. Find the direction and magnitude to `vecB` at the origin.

Text Solution

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`vecB=vecB_(xy)+vecB_(yz)+vecB_(zx)=((mu_0)/(4pi)(I)/(R)pi/2hatk)+((mu_0)/(4pi)I/Rpi/2hati)+((mu_0)/(4pi)I/Rpi/2hatj)=(mu_0)/(4pi)I/Rpi/2(hati+hatj+hatk)`
`=(mu_0I)/(8R)(hati+hatj+hatk)`
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