1
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b. The two loops are in the same plane. The outer loop of radius b carries an alternating current I = Io cos ($$\omega$$t). The emf induced in the smaller inner loop is nearly :
A
$${{\pi {\mu _o}{I_o}} \over 2}.{{{a^2}} \over b}\,\omega \sin \left( {\omega t} \right)$$
B
$${{\pi {\mu _o}{I_o}} \over 2}.{{{a^2}} \over b}\,\omega \cos \left( {\omega t} \right)$$
C
$$\pi {\mu _o}{I_o}\,{{{a^2}} \over b}\omega \sin \left( {\omega t} \right)$$
D
$${{\pi {\mu _o}{I_o}\,{b^2}} \over a}\omega \cos \left( {\omega t} \right)$$
2
JEE Main 2017 (Offline)
+4
-1
In a coil of resistance 100 $$\Omega$$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is:

A
275 Wb
B
200 Wb
C
225 Wb
D
250 Wb
3
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
$${{{\pi ^2}{r^4}B_0^2} \over {\tau R}}$$
4
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 = $${{ { \in _0}\upsilon B} \over 2},$$
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