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

Options

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

Answer

D

Explanation

Magnetic field at the centre M due to
current through the curved portion DA is

`B_(1)=(mu_(0)I)/(4piR)xx((3pi)/(2))` into the plane of the paper
Magnetic field at the centre M due to current through the straight portion AM is `B_(2)=1`
Since point M lies on the axis of the straight portion AB
Magnetic field at the centre M due to current through the curved portion BC is
`B_(3)=(mu_(0)I)/(4pi2R)xxpi/2` into the plane of the paper
`(mu_(0)I)/(16R)` into the plane of the paper
Magnetic field at the centre M due to current through the straight portion CD is `B_(4)=0`
Since point M lies on the axis of thge straight portion CD
The resultant magnetic field at the M is
`BB=B_(1)+B_(2)+B_(3)+B_(4)`
`=(3mu_(0)I)/(8R)+0+(mu_(0)I)/(16R)+0=(3mu_(0)I)/(8R)+(mu_(0I))/(16R)`
`=(7mu_(0)I)/(16R)` into the plane of the paper