1
JEE Main 2016 (Offline)
+4
-1
Two identical wires $$A$$ and $$B,$$ each of length $$'l'$$, carry the same current $$I$$. Wire $$A$$ is bent into a circle of radius $$R$$ and wire $$B$$ is bent to form a square of side $$'a'$$. If $${B_A}$$ and $${B_B}$$ are the values of magnetic fields at the centres of the circle and square respectively, then the ratio $${{{B_A}} \over {{B_B}}}$$ is:
A
$${{{\pi ^2}} \over {16}}$$
B
$${{{\pi ^2}} \over {8\sqrt 2 }}$$
C
$${{{\pi ^2}} \over {8}}$$
D
$${{{\pi ^2}} \over {16\sqrt 2 }}$$
2
JEE Main 2015 (Offline)
+4
-1
Two long current carrying thin wires, both with current $$I,$$ are held by insulating threads of length $$L$$ and are in equilibrium as shown in the figure, with threads making an angle $$'\theta '$$ with the vertical. If wires have mass $$\lambda$$ per unit-length then the value of $$I$$ is :
($$g=$$ $$gravitational$$ $$acceleration$$ )

A
$$2\sqrt {{{\pi gL} \over {{\mu _0}}}\tan \theta }$$
B
$$\sqrt {{{\pi \lambda gL} \over {{\mu _0}}}\tan \theta }$$
C
$$\sin \theta \sqrt {{{\pi \lambda gL} \over {{\mu _0}\,\cos \theta }}}$$
D
$$2\sin \theta \sqrt {{{\pi \lambda gL} \over {{\mu _0}\,\cos \theta }}}$$
3
JEE Main 2015 (Offline)
+4
-1

A rectangular loop of sides $$10$$ $$cm$$ and $$5$$ $$cm$$ carrying a current $$1$$ of $$12A$$ is placed in different orientations as shown in the figures below :

If there is a uniform magnetic field of $$0.3$$ $$T$$ in the positive $$z$$ direction, in which orientations the loop would be in $$(i)$$ stable equilibrium and $$(ii)$$ unstable equilibrium ?

A
$$(B)$$ and $$(D)$$, respectively
B
$$(B)$$ and $$(C)$$, respectively
C
$$(A)$$ and $$(B)$$, respectively
D
$$(A)$$ and $$(C)$$, respectively
4
JEE Main 2014 (Offline)
+4
-1
A conductor lies along the $$z$$-axis at $$- 1.5 \le z < 1.5\,m$$ and carries a fixed current of $$10.0$$ $$A$$ in $$- {\widehat a_z}$$ direction (see figure). For a field $$\overrightarrow B = 3.0 \times {10^{ - 4}}\,{e^{ - 0.2x}}\,\,{\widehat a_y}\,\,T,$$ find the power required to move the conductor at constant speed to $$x=2.0$$ $$m$$, $$y=0$$ $$m$$ in $$5 \times {10^{ - 3}}s.$$ Assume parallel motion along the $$x$$-axis.
A
$$1.57W$$
B
$$2.97W$$
C
$$14.85$$ $$W$$
D
$$29.7W$$
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