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) ) (hati + hatj + hatk) `
B. `2 ( (mu_0I)/(2R ) ) (hati + hatj + hatk) `
C. `1/2 ( (mu_0 I)/(2R) ) (hati + hatj +hatk) `
D. `3 ( (mu_0 I)/(2R) ) (hati + hatj + hatk ) `

Answer

A

Explanation

Magnetic field due to quarter circle of radius R (carrying current) and lying in the positive quadrant of xy-plane i.e.
`vecB_1 = 1/4 ( (mu_0 I)/(2R) ) hatk `
Similarly, due to quarter circle lying in yz - plane and zx- plane.
`vecB_2 = 1/4 ( (mu_0 I)/(2R) ) hati , vecB_3 = 1/4 ( (mu_0 I)/(2R) ) hatj `
So, net magnetic field at the origin
`vecB = vecB_1 + vecB_3 = 1/4 ( (mu_0I)/(2R) ) (hati + hatj + hatk) `