1
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1

A copper rod of mass m slides under gravity on two smooth parallel rails, with separation l and set at an angle of $$\theta$$ with the horizontal. At the bottom rails are joined by a resistance R. There is a uniform magnetic field B normal to the plane of the rails, as shown in the igure. The terminal speed of the copper rod is :
A
$${{mg\,R\,\tan \,\theta } \over {{B^2}\,{l^2}}}$$
B
$${{mg\,R\,\cot \,\theta } \over {{B^2}\,{l^2}}}$$
C
$${{mg\,R\,\sin \,\theta } \over {{B^2}\,{l^2}}}$$
D
$${{mg\,R\,\cos \,\theta } \over {{B^2}\,{l^2}}}$$
2
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
At the center of a fixed large circular coil of radius R, a much smaller circular coil of radius r is placed. The two coils are concentric and are in the same plane. The larger coil carries a current I. The smaller coil is set to rotate with a constant angular velocity $$\omega$$ about an axis along their common diameter. Calculate the emf induced in their smaller coil after a time t of its start of rotation.
A
$${{{\mu _o}{\rm I}} \over {2\,R}}$$ $$\omega$$ $$\pi$$ r2 sin$$\omega$$ t
B
$${{{\mu _o}{\rm I}} \over {4\,R}}$$ $$\omega$$ $$\pi$$ r2 sin$$\omega$$ t
C
$${{{\mu _o}{\rm I}} \over {4\,R}}$$ $$\omega$$ r2 sin$$\omega$$ t
D
$${{{\mu _o}{\rm I}} \over {2\,R}}$$ $$\omega$$ r2 sin$$\omega$$ t
3
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
A uniform magnetic field B of 0.3 T is along the positive Z-direction. A rectangular loop (abcd) of sides 10 cm × 5 cm carries a current I of 12 A. Out of the following different orientations which one corresponds to stable equilibrium ?
A
B
C
D
4
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
$${{\pi {\mu _o}{I_o}\,{b^2}} \over a}\omega \cos \left( {\omega t} \right)$$
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