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.

Explanation

For the current carrying loop quarter circles of radius R, lying in the positive quadrants of the x-y plane
`B_(1)=(mu_(0))/(4pi)(I(pi//2))/(R)hatk=(mu_(0))/(4)(I)/(2R)hatk`
For the current carrying loop quarter circles of radius R, lying int he positive quadrants of the y-z plane
`B_(2)=(mu_(0))/(4)(I)/(2R)hati`
For The current carrying loop quarter circles of radius R, lying in the positive quadrants of the z-x plane
`B_(3)=(mu_(0))/(4)(I)/(2R)hati`
Current carrying loop consists of 3 identical quarter circles of radius R, lying in the positive quadrants of the x-y, y-y and z-z planes with their centres at the origin, joined together is equal to the vector sum of magnetic field due to each quarter and given by
`B=(1)/(4pi)(hati+hatj+hatk)(mu_(0)I)/(2R)`