Electro magnetism

Q.1 The magnetic flux through a stationary loop with resistance R varies during interval of time T as  = at (T – t). The heat generated during this time neglecting the inductance of loop will be (A) R 3T a 3 2 (B) R 3T a 2 2 (C) R 3 T a2 (D) RT a 3 2 Q.2 A wire as a parabola y = a x2 is located in a uniform magnetic field of inductance B, the vector B being perpendicular to the plane xy. At the moment t = 0 a connector starts translation wise from the parabola apex with a constant acceleration  to find the emf of electromagnetic induction in the loop this formed as a function of y (A) in = 2 By a 2 (B) in = By a 2 (C) in = 2 By a 2 (D) in = 2 By a Q.3 A square coil ABCD is placed in x-y plane with its centre at origin. A long straight wire, passing through origin, carries a current in negative z-direction. Current in this wire increases with time. The induced current in the coil is : (A) clockwise (B) anticlockwise (C) zero (D) alternating Q.4 A long straight conductor is placed along axis of a circular coil of radius R. If the current, as shown in figure, starts decreasing with time, the current induced in loop would be (A) clockwise (ACB) (B) anticlockwise (ABC) (C) can not be decided (D) there will be no induced current. Q.5 Figure shows a bar magnet and a long straight wire W, carrying current into the plane of paper. Point P is the point of intersection of axis of magnet and the line of shortest distance between magnet and the wire. If P is the midpoint of the magnet, then which of the following statements is correct ? (A) magnet experiences a torque in clockwise direction (B) magnet experiences a torque in anticlockwise direction (C) magnet experiences a force, normal to the line of shortest distance (D) magnet experiences a force along the line of shortest distance Q.6 A square coil ABCD is lying in xy plane with its centre at origin. A lng straight wire passing through origin carries a current i = 2t in negative z-direction. The induced current in the coil is (A) clockwise (B) anticlockwise (C) alternating (D) zeroQ.7 A negative charge is given to a nonconducting loop and the loop is rotated in the plane of paper about its centre as shown in figure. The magnetic field produced by the ring affects a small magnet placed above the ring in the same plane: (A) the magnet does not rotate (B) the magnet rotates clockwise as seen from below. (C) the magnet rotates anticlockwise as seen from below (D) no effect on magnet is there. Q.8 Two identical conductors P and Q are placed on two frictionless rails R and S in a uniform magnetic field directed into the plane. If P is moved in the direction shown in figure with a constant speed then rod Q (A) will be attracted towards P (B) will be repelled away from P (C) will remain stationary (D) may be repelled or attracted towards P Q.9 The figure shows an isosceles triangle wire frame with apex angle equal to/2. The frame starts entering into the region of uniform magnetic field B with constant velocity v at t= 0. The longest side of the frame is perpendicular to the direction of velocity. If i is the instantaneous current through the frame then choose the alternative showing the correct variation of i with time. (A) (B) (C) (D) Q.10 Two coils, X and Y, are linked such that emf E is induced in Y when the current in X is changing at the rate       dt dI I . If a current I0 is now made to flow through Y, the flux linked with X will be (A) EI0 I (B)       IE I0 (C) (E I ) I0 (D) EI I0  Q.11 A conducting rod moves with constant velocity  perpendicular to the long, straight wire carrying a current I as shown compute that the emf generated between the ends of the rod. (A) r l   I 0 (B) r l  2 I 0 (C) r l   I 2 0 (D) r l  4 I 0 Q.12 A conducting rod of length l moves with velocity  a direction parallel to a long wire carrying a steady current I. The axis of the rod is maintained perpendicular to the wire with near end a distance r away as shown in the fig. Find the emf induced in the rod. (A)   I 0 ln     r r l (B)    I 2 0 ln     r r l(C)   I 0 ln      l l r (D)  2I 0 ln     r r l Q.13 A metallic rod of length L and mass M is moving under the action of two unequal forces F1 and F2 (directed opposite to each other) acting at its ends along its length. Ignore gravity and any external magnetic field. If specific charge of electrons is (e/m), then the potential difference between the ends of the rod is steady state must be (A) eM mL F F 2 1  (B) eM mL ) F F ( 2 1  (C) [ eM mL ] ln [F1/F2] (D) None Q.14 Two parallel rigid wires are fixed at a distance ‘d’ apart, with each wire in a vertical position. The top ends of the two wires are connected through an ideal inductor of inductance L. A straight connector of mass M can slide freely up and down, maintaining electrical contact with the two wires, in a horizontal position. A uniform magnetic field exists perpendicular to the plane of the wires. If the connector is released from rest, the graph of its downward velocity with time is : (A) (B) (C) (D) Q.15 Two parallel long straight conductors lie on a smooth surface. Two other parallel conductors rest on them at right angles so as to form a square of side a initially. A uniform magnetic field B exists at right angles to the plane containing the conductors. They start moving out with a constant velocity v. If r is the resistance per unit length of the wire the current in the circuit will be (A) r Bv (B) v Br (C) Bvr (D) Bv Q.16 A conducting rod PQ of length 5 m oriented as shown in figure is moving with velocity (2 m/s) i ˆwithout any rotation in a uniform magnetic field ) k ˆ4 j ˆ 3 (  Tesla. Emf induced in the rod is (A) 32 Volts (B) 40 Volt (C) 50 Volt (D) none Q.17 An equilateral triangular loop ADC of some finite magnetic field B  as shown in the figure. At time t = 0, side DC of loop is at edge of the magnetic field. Magnetic field is perpendicular to the paper inwards (or perpendicular to the plane of the coil). The induced current versus time graph will be as (A) (B) (C) (D) Q.18 The magnetic field in a region is given by B = B0 1 FH G IK Jxa k . A square loop of edge -length d is placed with its edge along x & y axis. The loop is moved with constant velocity VV i  0  . The emf induced in the loop is (A) V B d a 0 0 2 (B) V B d a 0 0 2 2 (C) V B a d 0 0 2 (D) NoneQ.19 A metal disc rotates freely, between the poles of a magnet in the direction indicated. Brushes P and Q make contact with the edge of the disc and the metal axle.What current, if any, flows through R? (A) a current from P to Q (B) a current from Q to P (C) no current, because the emf in the disc is opposed by the back emf (D) no current, because the emf induced in one side of the disc is opposed by the emf induced in the other side. (E) no current, because no radial emf is induced in the disc Q.20 A rectangular coil of single turn, having area A, rotates in a uniform magnetic field B an angular velocity  about an axis perpendicular to the field. If initially the plane of coil is perpendicular to the field, then the average induced e.m.f. when it has rotated through 90° is (A)  BA (B)  2BA (C)  4BA (D)  BA 2ANSWER Q.1 A Q.2 A Q.3 C Q.4 D Q.5 D Q.6 D Q.7 B Q.8 A Q.9 D Q.10 B Q.11 B Q.12 D Q.13 A Q.14 A Q.15 A Q.16 A Q.17 B Q.18 A Q.19 A Q.20 D