Electromagnetic Induction

In the given circuit below inductance values of L1, L2 and L3 are same. The magnetic energy stored in the entire circuit is (Ut) and that stored in the L2 inductor is (Ul). Ut/Ul is . (Ignore the mutual inductance if any) [figure]

A circular loop of radius 20 cm and resistance 2 is placed in a time varying magnetic field B= (2t2+2t+3 ) T. At t=0, for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at t=3 s is 50 A. The value of is . (Take =22/7)

A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in a uniform magnetic field of 2 T. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of 60 with vertical, then maximum induced EMF between the point of suspension and point of oscillation is mV. (Take g = 10 m/s2)

Inductance of a coil with 104 turns per metre is 10 mH and it is connected to a dc source of 10 V with internal resistance of 10 . The energy density in the inductor when the current reaches ( 1e ) of its maximum value is 1e2 J/m3. The value of is . ( 0 = 4 10-7 T m/A).

A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5 T perpendicular to the axis of rotation. When the loop is rotated by 30 from the horizontal position, the induced EMF is 15.4 mV. The radius of the loop is mm. (Take = 227)

Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of 1 2 Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of 10 cm/s, induced emf between points A and E is mV. [figure]

[figure] A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time t = 0 with a constant velocity. If the induced EMF is E tn, then value of n is .