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 ( MA =R, MB =2 R, angle DMA =90°)

Question

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 ( MA =R, MB =2 R, angle DMA =90°) <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-jgbepeyewyixmalt.jpg" /> (A) (5/16)(μ o i/R), but out of the plane of the paper (B) (5/16) (μ o i/R) , but into the plane of the paper (C) (7/16)(μ o i/R), but out of the plane of the paper (D) (7/16)(μ o i/R), but into the plane of the paper

Tardigrade Admin · Accepted Answer

(i) The magnetic field at the centre due to the curved portion

D A = \frac{( μ ) _{0} i}{4 π R} (\frac{3 π}{2})

According to the right-hand screw rule, the magnetic field will be into the plane of the paper.
Solution

(ii) The magnetic field at

M

due to

A B

is zero.
(iii) The magnetic field at the centre due to the curved portion

BC

is

\frac{( μ ) _{0} i}{4 π 2 R} (\frac{π}{2})

.
According to the right-hand screw rule, the magnetic field will be into the plane of the paper.
(iv) The magnetic field at

M

due to

D C

is zero.
Hence, the resultant magnetic field at

M

B_{M} = B_{small loop} + B_{big loop}

Both are perpendicular downward

B_{M} = \frac{( μ ) _{o^{i}}}{4 π R} (\frac{3}{2} π) + \frac{( μ ) _{o} i}{4 π ( 2 R )} (\frac{π}{2})

B_{M} = \frac{7}{16} \frac{μ _{O} i}{R} \otimes

Q. 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
$(M A = R, MB = 2 R, ∠ D M A = 9 0^{\circ})$

$\frac{5}{16} \frac{μ _{o} i}{R},$ but out of the plane of the paper

$\frac{5}{16} \frac{μ _{o} i}{R},$ but into the plane of the paper

$\frac{7}{16} \frac{μ _{o} i}{R},$ but out of the plane of the paper

$\frac{7}{16} \frac{μ _{o} i}{R},$ but into the plane of the paper

Q. 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 (MA=R,MB=2R,∠DMA=90∘)

165​Rμo​i​, but out of the plane of the paper

165​Rμo​i​, but into the plane of the paper

167​Rμo​i​, but out of the plane of the paper

167​Rμo​i​, but into the plane of the paper

Q. 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
$(M A = R, MB = 2 R, ∠ D M A = 9 0^{\circ})$

$\frac{5}{16} \frac{μ _{o} i}{R},$ but out of the plane of the paper

$\frac{5}{16} \frac{μ _{o} i}{R},$ but into the plane of the paper

$\frac{7}{16} \frac{μ _{o} i}{R},$ but out of the plane of the paper

$\frac{7}{16} \frac{μ _{o} i}{R},$ but into the plane of the paper