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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 of B at the origin. |
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Answer» Solution :1. I current carrying ARC having a radius R SUBTEND ANGLE `theta` at centre point then, magnetic field is given by `B=(mu_(0)Itheta)/(4piR)`. 2. Magnetic field at O from current carrying loop at xy-plane, `vecR_(n)=(mu_(0)I)/(4piR)(pi/2)hatk` `vecR_(n)=(mu_(0)I)/(4(2R))hatk` 3. Magnetic field at O from current carrying loop at yz-plane, `vecR_(n)=(mu_(0)I)/(4(2R))hati` 4. Magnetic field at O from current carrying at zx-plane, `thereforevecR_(n)=(mu_(0)I)/(4(2R))hatj` `thereforevecR_(n)=vecR_(1)+vecR_(2)+vecR_(3)` = `(mu_(0)I)/(4(2R))(hati+hatj+hatk)` `vecR_(n)=(mu_(0)I)/(8R)(hati+hatj+hatk)` 
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