A current `I` is flowing thorugh the loop. The direction of the current and the shape of the loop are as the shown in the figure. The magnetic fild at the centre of the loop is `(mu_(0) I)/(R)` times
`(MA = R, MB = 2R, /_DMA = 90^(@))`

Options

A. `(5)/(16)`, but out of the plane of the paper.
B. `(7)/(16)`, but into of the plane of the paper.
C. `(5)/(16)`, but into of the plane of the paper.
D. `(7)/(16)`, but out of the plane of the paper.

Answer

B

Explanation

Magnetic field at the centre `M` due to current through the curved portion `DA` is
`vec(B)_(i) = (mu_(0)I)/(4pi R) xx ((3pi)/(2)) = (3mu_(0) I)/(8R) ox`
[into the plane of paper]

Magnetic field at the centre `M` due to current though the staight portion `AB` and `CD` will be zero.
Magnetic field at the centre `M` due to current through the curved portion `BC`is
`vec(B)_(i) = (mu_(0) I)/(4pi 2R) xx (pi)/(2) = (mu_(0) I)/(16 R) ox` [into the plane of paper]
The resultant magnetic field at the point `M` is
`vec(B) = vec(B)_(1) + vec(B)_(2) = ((3mu_(0) I)/(8R) + (mu_(0) I)/(16R))ox = (7mu_(0) I)/(16R) ox`
[into the plane of paper]