A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius = b) and

Q: A current loop $ABCD$ is held fixed on the plane of the paper as shown in the figure. The arcs $ BC$ (radius $= b$) and $DA $ (radius $= a$) of the loop are joined by two straight wires $AB $ and $CD$. A steady current $I$ is flowing in the loop. Angle made by $AB$ and $CD$ at the origin $O$ is $30^o $. Another straight thin wire with steady current $I_1$ flowing out of the plane of the paper is kept at the origin. The magnitude of the magnetic field $(B)$ due to the loop $ABCD$ at the origin $(O)$ is :

b The magnetic field at $O$ due to current in $D A$ is $B_{1}=\frac{\mu_{o}}{4 \pi} \frac{I}{a} \times \frac{\pi}{6} \quad$ (directed verticallyupwards) The magnetic field at $O$ due to current in $B C$ is $B_{2}=\frac{\mu_{o}}{4 \pi} \frac{I}{b} \times \frac{\pi}{6} \quad$ (directed vertically downwards) The magnetic field due to current $A B$ and $C D$ at $O$ is zero. Therefore the net magnetic field is $B=B_{1}-B_{2} \quad$ (directed vertically upwards) $=\frac{\mu_{o}}{4 \pi} \frac{I}{a} \frac{\pi}{6}-\frac{\mu_{o}}{4 \pi} \frac{I}{b} \times \frac{\pi}{6}=\frac{\mu_{o} I}{24}\left(\frac{1}{a}-\frac{1}{b}\right)=\frac{\mu_{o} I}{24 a b}(b-a)$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

A current loop $ABCD$ is held fixed on the plane of the paper as shown in the figure. The arcs $ BC$ (radius $= b$) and $DA $ (radius $= a$) of the loop are joined by two straight wires $AB $ and $CD$. A steady current $I$ is flowing in the loop. Angle made by $AB$ and $CD$ at the origin $O$ is $30^o $. Another straight thin wire with steady current $I_1$ flowing out of the plane of the paper is kept at the origin.

The magnitude of the magnetic field $(B)$ due to the loop $ABCD$ at the origin $(O)$ is :

A$0$
B$\frac{{{\mu _0}I(b - a)}}{{24ab}}$
C$\frac{{{\mu _0}I}}{{4\pi }}\left[ {\frac{{b - a}}{{ab}}} \right]$
D$\frac{{{\mu _0}I}}{{4\pi }}\left[ {2(b - a) + \frac{{\pi (a + b)}}{3}} \right]$

AIEEE 2009, Diffcult

STD 11 Science
NEET
STD 12 - 4. Moving charges and magnetism
Physics

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