Title 1. ELECTROMAGNETISM & EMI_Final (PART-II) (39-67).pdf ✅

IIT ADVANCED NAME OF THE TOPIC NISHITH Multimedia India (Pvt.) Ltd., 3 9 JEE MAINS - CW - VOL - I ELECTROMAGNETISM & EMI NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL-VII LEVEL- VI SINGLE ANSWER QUESTIONS BIOT-SAVART’S LAW & FORCE ON CONDUCTOR 1 A square frame carrying a current I is located in the same plane as a long straight wire carrying a current 0 I . The frame side has a length a. The axis of the frame passing the midpoints of opposite sides is parallel to the wire and is separated from it by the distance which is  1.5 times greater than the side of the frame. Find the mechanical work to be performed in order to turn the frame through 0 180 about its axis, with currents maintained constant. (a)     0 0 log 2 e  II a  (b)     0 0 log 3 e  II a  (c)     0 0 log 5 e  II a  (d)     0 0 log 4 e  II a  2. A wire carrying a current I is bent into the shape of an exponential spiral, r e   , from   0 to   2 as shown in figure (a). To complete a loop, the ends of the spiral are connected by a straight wire along the x-axis. Find the magnitude and direction of B  at the origin. (a)   0 2 1 4 I e      (b)   0 2 1 3 I e      (c)   0 2 1 I e      (d)   0 2 1 2 I e      3. The figure shows a right angled isosceles triangle wire frame. The wire frame starts entering into the region of uniform magnetic field with constant velocity v at t  0. If I is the instantaneous current through the frame, then choose the correct graph between I and t. t  0 a v                         A. 2 a v t l B. 2 a v t l C. 2 a v t l D. 2 a v t l EMI 4. A conducting rod PQ of mass m and length l is placed on two long parallel (smooth and conducting) rails connected to a capacitor as shown. The rod PQ is connected to a non conducting spring of spring constant k, which is initially in relaxed state. The entire arrangement is placed in a magnetic field perpendicular to the plane of figure. Neglect the resistance of the rails and rod. Now, the rod is imparted a velocity 0 v towards right, then acceleration of the rod as a function of its displacement x is given by 0 v P  Q                                                A. kx m B. 2 2 kx m B l C  C. 2 2 kx m B l C  D. None of these
4 0 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL-VII NISHITH Multimedia India (Pvt.) Ltd., ELECTROMAGNETISM & EMI 5. A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current I passes through the coil, the magnetic field at the centre is. (A) b μ NI 0 (B) a 2μ NI 0 (C)   a b ln 2 b a μ NI 0  (D)   0 ln . IN b b a a   6. A rectangular loop with a sliding conductor of length l is located in a uniform magnetic field perpendicular to the plane of the loop. The magnetic induction is B. The conductor has a resistance R. The sides AB and CD have resistances R1 and R2 , respectively. Find the current through the conductor during its motion to the right with a constant velocity v . X X X x X X X X X X X X X X X X X X X X R1 R2 X X X X X v A B D C A.     1 2 1 1 2 Blv R R R R R   B. 2 1 1 2 Bl v R R R  C.     1 2 1 2 1 2 Blv R R R R R R R    D.   2 1 2 1 2 Bl v R R R R R   7. A copper rod is bent into a semi-circle of radius a and at ends straight parts are bent along diameter of the semi-circle and are passed through fixed, smooth and conducting ring O and O' as shown in figure. A capacitor having capacitance C is connected to the rings. The system is located in a uniform magnetic field of induction B such that axis of rotation OO' is perpendicular to the field direction. At initial moment of time (t=0), plane of semi-circle was normal to the field direction and the semi-circle is set in rotation with constant angular velocity  . Neglect the resistance and inductance of the circuit. The current flowing through the circuit as function of time is X B O O 1 C A. 1 2 2 cos 4   a CB t B. 1 2 2 cos 2   a CB t C. 1 2 2 sin 4   a CB t D. 1 2 2 sin 2   a CB t 8. A rectangular loop of wire with dimensions shown in figure is coplanar with a long wire carrying current I. The distance between the wire and the left side of the loop is r. The loop is pulled to the right as indicated. What are the directions of the induced current in the loop and the magnetic forces on the left and the right sides of the loop when the loop is pulled? r b a I Induced current Force on left side Force on right side A. Counterclockwise To the left To the left B. Counterclockwise To the right To the left C. Clockwise To the right To the left D. Clockwise To the left To the right