1
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
A conducting metal circular-wire-loop of radius r is placed perpendicular to a magnetic field which varies with time as
B = B0e$${^{{{ - t} \over r}}}$$ , where B0 and $$\tau$$ are constants, at time t = 0. If the resistance of the loop is R then the heat generated in the loop after a long time (t $$\to$$ $$\infty$$) is :
A
$${{{\pi ^2}{r^4}B_0^4} \over {2\tau R}}$$
B
$${{{\pi ^2}{r^4}B_0^2} \over {2\tau R}}$$
C
$${{{\pi ^2}{r^4}B_0^2R} \over \tau }$$
D
$${{{\pi ^2}{r^4}B_0^2} \over {\tau R}}$$
2
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed ‘v’ in a uniform magnetic field B going into the plane of the paper (See figure). If charge densities $$\sigma$$1 and $$\sigma$$2 are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects) :

A
$$\sigma$$1 = $$\in$$0 $$\upsilon$$ B, $$\sigma$$2 = $$-$$ $$\in$$0 $$\upsilon$$ B
B
$$\sigma$$1 = $${{{ \in _0}\upsilon \,B} \over 2},$$ $$\sigma$$2 = $${{ - { \in _0}\,\upsilon B} \over 2}$$
C
$$\sigma$$1 = $$\sigma$$2 = $${ \in _0}\,\upsilon B$$
D
$$\sigma$$1 = $${{ - { \in _0}\upsilon B} \over 2},$$ $$\sigma$$2 = $${{ { \in _0}\upsilon B} \over 2},$$
3
JEE Main 2015 (Offline)
+4
-1
Two coaxial solenoids of different radius carry current $$I$$ in the same direction. $$\overrightarrow {{F_1}}$$ be the magnetic force on the inner solenoid due to the outer one and $$\overrightarrow {{F_2}}$$ be the magnetic force on the outer solenoid due to the inner one. Then :
A
$$\overrightarrow {{F_1}}$$ is radially in wards and $$\overrightarrow {{F_2}} = 0$$
B
$$\overrightarrow {{F_1}}$$ is radially outwards and $$\overrightarrow {{F_2}} = 0$$
C
$$\overrightarrow {{F_1}} = \overrightarrow {{F_2}} = 0$$
D
$$\overrightarrow {{F_1}}$$ is radially inwards and $$\overrightarrow {{F_2}}$$ is radially outards
4
JEE Main 2013 (Offline)
+4
-1
A circular loop of radius $$0.3$$ $$cm$$ lies center of the small loop is on the axis of the bigger loop. The distance between their centers is $$15$$ $$cm.$$ If a current of $$2.0$$ $$A$$ flows through the smaller loop, than the flux linked with bigger loop is
A
$$9.1 \times {10^{ - 11}}\,$$ weber
B
$$6 \times {10^{ - 11}}\,$$ weber
C
$$3.3 \times {10^{ - 11}}\,$$ weber
D
$$6.6 \times {10^{ - 9}}\,$$ weber
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