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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

AI Generated Solution

To find the direction and magnitude of the magnetic field \(\vec{B}\) at the origin due to a current-carrying loop consisting of three identical quarter circles, we can follow these steps: ### Step 1: Understand the Configuration We have three identical quarter circles of radius \(R\) located in the positive quadrants of the x-y, y-z, and z-x planes. Each quarter circle contributes to the magnetic field at the origin. ### Step 2: Magnetic Field Due to a Full Circle The magnetic field at the center of a complete circular loop carrying current \(I\) is given by the formula: \[ ...
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Knowledge Check

  • A 4 A current carrying loop consists of three identical quarter circles of radius 5 cm lying in the positive quadrants of the x-y, y-z and z-x planes with their centres at the origin joined together, value of B at the origin is

    A
    `(mu_(0))/(10)(hati+hatj-hatk)T`
    B
    `(mu_(0))/(10)(-hati+hatj+hatk)T`
    C
    `(mu_(0))/(5)(hati+hatj+hatk)T`
    D
    `10mu_(0)(hati+hatj+hatk)T`

  • 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 `vec(B)` at `(0,0,z),zgtgtR` increases.
    D
    The magnitude of `vec(B)` at `(0,0,z), zgtgtR` is unchanged.

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