1
AIEEE 2011
+4
-1
A current $$I$$ flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius $$R.$$ The magnitude of the magnetic induction along its axis is:
A
$${{{\mu _0}I} \over {2{\pi ^2}R}}$$
B
$${{{\mu _0}I} \over {2\pi R}}$$
C
$${{{\mu _0}I} \over {4\pi R}}$$
D
$${{{\mu _0}I} \over {{\pi ^2}R}}$$
2
AIEEE 2010
+4
-1
Two long parallel wires are at a distance $$2d$$ apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field $$B$$ along the line $$XX'$$ is given by
A
B
C
D
3
AIEEE 2009
+4
-1
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 $${30^ \circ }.$$ Another straight thin wire 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
$${{{\mu _0}I\left( {b - a} \right)} \over {24ab}}$$
B
$${{{\mu _0}I} \over {4\pi }}\left[ {{{b - a} \over {ab}}} \right]$$
C
$${{{\mu _0}I} \over {4\pi }}\left[ {2\left( {b - a} \right) + {\raise0.5ex\hbox{\scriptstyle \pi } \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 3}}\left( {a + b} \right)} \right]$$
D
zero
4
AIEEE 2009
+4
-1
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 $${30^ \circ }.$$ Another straight thin wire steady current $${I_1}$$ flowing out of the plane of the paper is kept at the origin.

Due to the presence of the current $${I_1}$$ at the origin:

A
The forces on $$AD$$ are $$BC$$ are zero.
B
The magnitude of the net force on the loop is given by $${{{I_1}I} \over {4\pi }}{\mu _0}\left[ {2\left( {b - a} \right) + {\raise0.5ex\hbox{\scriptstyle \pi } \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 3}}\left( {a + b} \right)} \right].$$
C
The magnitude of the net force on the loop is given by $${{{\mu _0}I{I_1}} \over {24ab}}\left( {b - a} \right).$$
D
The forces on $$AB$$ and $$DC$$ are zero.
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