Electromagnetic Induction · Question 5

Consider a circuit consisting of a capacitor of capacitance C and a coil with N turns per unit length, cross sectional area S and length d, where d2 S. There is another coil of length d/2, cross sectional area S/2 and 2N turns per unit length completely inside the larger coil, as shown in the figure. The ends of this smaller coil are connected with each other by an insulated conducting wire. The self-inductance of the larger coil is L. Neglecting edge effects and all the Ohmic resistances, the resonant frequency of the circuit is: [figure]

1. 4 15 LC
2. 6 5 LC
3. 2 3 LC
4. 23 LC

List-I contains four conducting loops lying in the XY plane, as shown in the figures. The loops are rotating about Z axis passing through the point O with time period T in clockwise direction. The region x > 0 contains a uniform magnetic field B in the +z direction. List-II contains the qualitative variation of the induced current i(t) for each of these loops. Choose the option which describes the correct match between the entries in List-I to those in List-II.

1. P → 5, Q → 4, R → 1, S → 3
2. P → 3, Q → 2, R → 5, S → 4
3. P → 3, Q → 2, R → 1, S → 4
4. P → 5, Q → 1, R → 2, S → 3

A conducting square loop initially lies in the XZ plane with its lower edge hinged along the X-axis. Only in the region y 0, there is a time dependent magnetic field pointing along the Z-direction, B(t)=B0( t) k, where B0 is a constant. The magnetic field is zero everywhere else. At time t=0, the loop starts rotating with constant angular speed about the X axis in the clockwise direction as viewed from the +X axis (as shown in the figure). Ignoring self-inductance of the loop and gravity, which of the following plots correctly represents the induced e.m.f. (V) in the loop as a function of time: [figure]

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A conducting square loop of side L, mass M and resistance R is moving in the XY plane with its edges parallel to the X and Y axes. The region y 0 has a uniform magnetic field, B=B0 k. The magnetic field is zero everywhere else. At time t=0, the loop starts to enter the magnetic field with an initial velocity v0 j m/s, as shown in the figure. Considering the quantity K= B02L2RM in appropriate units, ignoring self-inductance of the loop and gravity, which of the following statements is/are correct: [figure]

1. If v0=1.5KL, the loop will stop before it enters completely inside the region of magnetic field.
2. When the complete loop is inside the region of magnetic field, the net force acting on the loop is zero.
3. If v0= KL10, the loop comes to rest at t= ( 1K ) ( 52 ).
4. If v0=3KL, the complete loop enters inside the region of magnetic field at time t= ( 1K ) ( 32 ).