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 (μ0I/R) times (MA=R, MB = 2R, angle DCM = 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 (μ0I/R) times (MA=R, MB = 2R, angle DCM = 90°) (A) (5/16), but out of the plane of the paper (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

Tardigrade Admin · Accepted Answer

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

B_{1} = \frac{μ _{0} I}{4 π R} \times (\frac{3 π}{2})

= \frac{3 μ _{0} I}{8 R} \otimes

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

B_{2} = 0

, 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} = \frac{μ _{0} I}{4 π 2 R} \times \frac{π}{2} = \frac{μ _{0} I}{16 R} \otimes

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

B_{4} = 0

, sincepoint M lies on the axis of the straight portion CD.
The resultant magnetic field at the point M is

B = B_{1} + B_{2} + B_{3} + B_{4}

= (\frac{3 μ _{0} I}{8 R} + 0 + \frac{μ _{0} I}{16 R} + 0) \otimes = \frac{7 μ _{0} I}{16 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 $\frac{μ _{0} I}{R}$ times
$(M A = R, MB = 2 R, ∠ D CM = 9 0^{\circ})$

$\frac{5}{16},$ but out of the plane of the paper

$\frac{5}{16},$ but into the plane of the paper

$\frac{7}{16},$ but out of the plane of the paper

$\frac{7}{16},$ 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 Rμ0​I​ times (MA=R,MB=2R,∠DCM=90∘)

165​, but out of the plane of the paper

165​, but into the plane of the paper

167​, but out of the plane of the paper

167​, 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 $\frac{μ _{0} I}{R}$ times
$(M A = R, MB = 2 R, ∠ D CM = 9 0^{\circ})$

$\frac{5}{16},$ but out of the plane of the paper

$\frac{5}{16},$ but into the plane of the paper

$\frac{7}{16},$ but out of the plane of the paper

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