1
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
$$2\sin \theta \sqrt {{{\pi \lambda gL} \over {{\mu _0}\,\cos \theta }}}$$
2
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
3
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
$$29.7W$$
4
AIEEE 2012
+4
-1
Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, denuteron and alpha particle are respectively $${r_p},{r_d}$$ and $${r_\alpha }$$. Which one of the following relation is correct?
A
$${r_\alpha } = {r_p} = {r_d}$$
B
$${r_\alpha } = {r_p} < {r_d}$$
C
$${r_\alpha } > {r_d} > {r_p}$$
D
$${r_\alpha } = {r_d} > {r_p}$$
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