1
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
2
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.
3
AIEEE 2008
+4
-1
A horizontal overhead powerline is at height of $$4m$$ from the ground and carries a current of $$100A$$ from east to west. The magnetic field directly below it on the ground is
$$\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,\,Tm\,\,{A^{ - 1}}} \right)$$
A
$$2.5 \times {10^{ - 7}}\,T$$ southward
B
$$5 \times {10^{ - 6}}\,T$$ northward
C
$$5 \times {10^{ - 6}}\,T$$ southward
D
$$2.5 \times {10^{ - 7}}\,T$$ northward
4
AIEEE 2007
+4
-1
A charged particle with charge $$q$$ enters a region of constant, uniform and mutually orthogonal fields $$\overrightarrow E$$ and $$\overrightarrow B$$ with a velocity $$\overrightarrow v$$ perpendicular to both $$\overrightarrow E$$ and $$\overrightarrow B,$$ and comes out without any change in magnitude or direction of $$\overrightarrow v$$. Then
A
$$\overrightarrow v = \overrightarrow B \times \overrightarrow E /{E^2}$$
B
$$\overrightarrow v = \overrightarrow E \times \overrightarrow B /{B^2}$$
C
$$\overrightarrow v = \overrightarrow B \times \overrightarrow E /{B^2}$$
D
$$\overrightarrow v = \overrightarrow E \times \overrightarrow B /{E^2}$$
EXAM MAP
Medical
NEET