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.

Options

A. `(1)/(4)((mu_(0)I)/(2R))(hat(i)+hat(j)+hat(k))`
B. `2((mu_(0)I)/(2R))(hat(i)+hat(j)+hat(k))`
C. `(1)/(2)((mu_(0)I)/(2R))(hat(i)+hat(j)+hat(k))`
D. `3((mu_(0)I)/(2R))(hat(i)+hat(j)+hat(k))`

Answer

1

Explanation

Magnetic field due to quarter circle of radius `R` ( carrying current ) and lying in the positive quadrant of `xy-` plane `i.e.`
`vec(B)_(1)=(1)/(4)((mu_(0)I)/(2R))hat(k)`
Similarly, due to quarter circle lying in `yz-` plane and `zx-` plane.
`vec(B)_(2)=(1)/(4)((mu_(0)I)/(2R))hat(i),vec(B)_(3)=(1)/(4)((mu_(0)I)/(2R))hat(j)`
So, net magnetic field at the origin
`vec(B)=vec(B)_(1)+vec(B)_(3)=(1)/(4)((mu_(0)I)/(2R))(hat(i)+hat(j)+hat(k))`