Question

A current I is flowing through a 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 $\frac { \mu _ { 0 } I } { R }$ times

(Here, MA = R, MB = 2R,< DMA = 90°)

• A. $\frac { 5 } { 16 }$ , out of the plane of the paper.
• B. $\frac { 5 } { 16 }$, into the plane of the paper.
• C. $\frac { 7 } { 16 }$, out of the plane of the paper.
• D. $\frac { 7 } { 16 }$, into the plane of the paper.

Answer 1

Answer: (D)

$\frac { 7 } { 16 }$, into the plane of the paper.

Answer 2

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

into the plane of the paper

into the plane of the paper

Magnetic field at the centre M due to current through the straight portion AB is

( point M lies on the axis of the straight line portion AB) Magnetic field at centre M due to current through the curbed portion BC is

$\mathrm { B } _ { 3 } = \frac { \mu _ { 0 } \mathrm { I } } { 4 \pi ( 2 \mathrm { R } ) } \times \frac { \pi } { 2 }$ into the plane of the paper

into the plane of the paper

Magnetic field at the centre M due to current through the straight portion CD is

( point M lies on the axis of the straight portion CD)

The resultant magnetic field at M is

into the plane of the paper