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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 of B at the origin.

Text Solution

Verified by Experts

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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Knowledge Check

  • A current carrying circular loop of radius R is placed in the x-y plane with centre at the origin. Half of the loop with xgt0 is now bent so that it now lies in the y-z plane.

    A
    The magnitude of magnetic moment now diminishes.
    B
    The magnetic moment does not change.
    C
    The magnitude of B at `(0,0,z),zgtgtR` increases.
    D
    The magnitude of B at `(0,0,z),zgtgtR` is unchanged.

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