2.ELECTRODYNAMICS-PART TEST - 1

PART TEST - 1 (PT-1) TOPIC : ELECTRODYNAMICS (PHYSICS) Duration : 1 Hour Max. Marks : 90 GENERAL INSTRUCTIONS 1. This Question Paper contains 30 objective type questions. 2. Each question has 4 choices (A), (B), (C) and (D), out of which only one is correct. 3. For each question, you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. SECTION - I Straight Objective Type This section contains 30 Single choice questions. Each question has choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. A and C are concentric conducting spherical shells of radius a and c respectively. A is surrounded by a concentric dielectric medium of inner radius a, outer radius b and dielectric constant K as shown in the figure. If sphere A is given a charge Q, the potential at the outer surface of the dielectric is. Q Q  1 1  (A) 4 kb (B) 4    a k(b  a) 0 0   (C) Q 40b (D) None of these 2. In the given circuit the rms value of voltage across the capacitor C, inductor L and resister R1 are 12V, 10V and 5V respectively. Then the peak voltage across R2 is (A) 7 2V (D) none of these 3. Two identical capacitors C1 and C2 are connected in series with a battery. They are fully charged. Now a dielectric slab is inserted between the plates of C2. The potential difference across C1 will : (A) increase (B) decrease (C) remain same (D) depend on internal resistance of the cell 9. There exists a uniform electric field in the space as shown. Four points A, B, C and D are marked which are equidistant from the origin. If VA, VB, VC and VD are their potentials respectively, then x (A) VB > VA > VC > VD (B) VA > VB > VD > VC (C) VA = VB > VC = VD (D) VB > VC > VA > VD 10. A current carrying wire AB of the length L is turned along a circle, as shown in figure. The magnetic field at the centre O.  i  2  2 0 i  2    (A) 0   (B)   L  2  L  2  (C) 0i (2 – ) (D) 0i (2 + )2 L L 11. Total electric force on an electric dipole placed in an electric field of a point charge is: (A) always zero (B) never zero (C) zero when mid point of dipole coincides with the point charge (D) zero when dipole axis is along any electric line of force. 12. The magnitude of magnetic field at O (centre of the circular part) due to the current carrying coil as shown is : (A) 0i  3  (B) 0i  3  b 4  a  2  2a  (C) 0i    (D) 0i  3  2  3a 2 b  4  2a  13. Eight point charges (can be assumed as small spheres uniformly charged and their centres at the corner of the cube) having values q each are fixed at vertices of a cube. The electric flux through square surface ABCD of the cube is (A) q 24 0 q (B) 12 0 q (C) 6 0 q (D) 8 0 14. A charged particle is moving in the region around a long current carrying wire. Due to wire, it may experience: (A) only magnetic force (B) only electric force (C) both electric force and magnetic force (D) magnetic force and gravitational force 21. The equivalent resistance between A and B will be (in ) (A) 2/7 (B) 8 (C) 4/3 (D) 7/3 22. As shown in figure, a permanent magnet and current carrying coil are placed. If the coil is moved towards magnet, then current in coil (Magnet is symmetrical) : (A) increases (B) decreases (C) remains same (D) first increases then decreases 23. In the figure shown: (A) current will flow from A to B (B) current may flow from A to B (C) current will flow from B to A (D) the direction of current will depend on r. 24. A super conducting loop having an inductance 'L' is kept in a magnetic field which is varying with respect to time. If  is the total flux,  = total induced emf, then: (A)  = constant (B)  = 0 (C)   0 (D) none of these 25. A battery of internal resistance ' r ' and e.m.f.  is connected to a variable external resistor AB. If the sliding contact is moved from A to B, then terminal potential difference of battery will : (A) remain constant & is independent of value of external resistance (B) increase continuously (C) decrease continuously (D) first increase and then will decrease. 26. Figure shows a conducting horizontal rod of resistance r is made to oscillate simple harmonically with a fixed amplitude in a uniform and constant magnetic field B, directed inwards. The ends of rod always touch two parallel fixed vertical conducting rails. The ends of rails are joined by an inductor and a capacitor having 1 1 self inductance and capacitance  Henry and  farad respectively. The amplitude of current in the circuit depends on the frequency of oscillation of rod. The amplitude of the current will be maximum when the time period of rod is : (do not consider self inductance anywhere other than in the inductor) (A) 0.5 sec (B) 1 sec (C) 2 sec (D) 4 sec A nswers 1. (C) 2. (C) 3. (A) 4. (A) 5. (A) 6. (A) 7. (A) 8. (C) 9. (B) 10. (A) 11. (B) 12. (D) 13. (C) 14. (D) 15. (A) 16. (C) 17. (A) 18. (B) 19. (D) 20. (A) 21. (D) 22. (C) 23. (B) 24. (A) 25. (B) 26. (C) 27. (B) 28. (C) 29. (A) 30. (B) 3. Figure shows a system of three concentric metal shells A, B and C with radii a, 2a and 3a respectively. Shell B is earthed and shell C is given a charge Q. Now i f shell C is connected to shell A, then the f inal charge on the shell B, is equal to : 4Q (A) – 13 (B) – 8Q 11 5Q (C) – 3 (D) – 3Q 7 4. A ring of mass m, radius r having charge q uniformly distributed over it and free to rotate about its own axis is placed in a region having a magnetic field B parallel to its axis. If the magnetic field is suddenly switched off, the angular velocity acquired by the ring is : (A) qB (B) m 2qB m (C) qB (D) None of these 2m 5. Four infinite ladder network containing identical resistances of R  each, are combined as shown in figure. The equivalent resistance between A and RAB B is RAB and between A and C is RAC. Then the value of R is : AC B C A D (A) 3 (B) 4 4 3 (C) 2 (D) 1 2 6. Two small balls, each having equal positive charge Q are suspended by two insulating strings of equal length L from a hook fixed to a stand. If the whole set-up is transferred to a satellite in orbit around the earth, the tension in equilibrium in each string is equal to kQ (A) zero (B) L2 (C) kQ2 2L2 (D) kQ2 4L2 7. In a practical wheat stone bridge circuit as shown, when one more resistance of 100  is connected in parallel with unknown resistance ' x ', then ratio 𝑙1/𝑙2 becomes '2'. 𝑙1 is balance length. AB is a uniform wire. Then value of ' x ' must be : (A) 50  (B) 100  (C) 200  (D) 400  11. In front of an earthed conductor a point charge + q is placed as shown in figure : (A) On the surface of conductor the net charge is always negative. (B) On the surface of conductor at some points charges are negative and at some points charges may be positive distributed non uniformly (C) Inside the conductor electric field due to point charge is non zero (D) None of these 12. In the figure shown the key is switched on at t = 0. Let  and  be the currents through inductors having self inductances L1 & L2 at any time t respectively. The magnetic energy stored in the inductors 1 and 2 be U1 U1 and U2. Then 2 at any instant of time is : V L1 L1 (A) 2  L2 (B) 1  R 1 (C) 2 2 (D) 1 SECTION - III Reasoning Type This section contains 4 Reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 13. Statement – 1 Four point charges q1, q2, q3 and q4 are as shown in figure. The flux over the shown Gaussian surface depends only on charges q1 and q2. q4 q1 Gaussian 2 surface 3 Statement – 2 Electric field at all points on Gaussian surface depends only on charges q1 and q2. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True. Paragraph for Question Nos. 17 to 19 In the circuit given below, both batteries are ideal. EMF E1 of battery 1 has a fixed value, but emf E2 of battery 2 can be varied between 1.0 V and 10.0 V. The graph gives the currents through the two batteries as a function of E2, but are not marked as which plot corresponds to which battery. But for both plots, current is assumed to be negative when the direction of the current through the battery is opposite the direction of that battery's emf. (Direction of emf is from negative to positive) 17. The value of emf E1 is : (A) 8 V (B) 6 V (C) 4 V (D) 2V 18. The resistance R1 has value : (A) 10  (B) 20  (C) 30  (D) 40  19. The resistance R2 is equal to : (A) 10  (B) 20  (C) 30  (D) 40  Paragraph for Question Nos. 20 to 22 Curves in the graph shown give, as functions of radial distance r (from the axis), the magnitude B of the magnetic field (due to individual wire) inside and outside four long wires a, b, c and d, carrying currents that are uniformly distributed across the cross sections of the wires. Overlapping portions of the plots are indicated by double labels. All curves start from the origin. B r 24. A square loop of uniform conducting wire is as shown in figure. A current-I ( in amperes) enters the loop from one end and exits the loop from opposite end as shown in figure. The length of one side of square loop is 𝑙 metre. The wire has uniform cross section area and uniform linear mass density. In four situations of column-I, the loop is subjected to four different uniform and constant magnetic field. Under the conditions of column-I, match the column-I with corresponding results of column-II ( Bo in column I is a positive nonzero constant) (A) (B) Column-I Column-II →  B ˆi in tesla (p) magnitude of net force on loop is →  B ˆj in tesla (q) magnitude of net force on loop is zero BoI 𝑙 newton → (C)  B (ˆi  ˆj) in tesla (r) magnitude of net torque on loop about its centre is zero (D) →  B kˆ in tesla (s) magnitude of net force on loop is BoI 𝑙 newton PART TEST - 3 (PT-3) TOPIC : ELECTRODYNAMICS (PHYSICS) Duration : 1 Hour Max. Marks : 90 GENERAL INSTRUCTIONS 1. This Question Paper contains 22 questions. 2. For each question in Section I, you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 3. For each question in Section II, you will be awarded 4 Marks if you give the correct answer. There is no negative marking. 4. For each question in Section III, you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 5. For each question in Section IV, you will be awarded 4 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 6. For each question in Section V, you will be awarded 6 Marks if you give ALL the correct answer(s) or awarded : (i) 1 Mark for correct answer in one row. (ii) 2 Marks for correct answer in two rows. (iii) 4 Marks for correct answer in three rows. 7. For each question in Section VI, you will be awarded 6 Marks if you give the correct answer. There is no negative marking. SECTION - I Straight Objective Type This section contains 8 Single choice questions. Each question has choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. In the figure shown a parallel plate capacitor has a dielectric of width d/2 and dielectric constant K = 2. The other dimensions of the dielectric are same as that of the plates. The plates P1 and P2 of the capacitor have area 'A' each. The energy of the capacitor is : (A) 0 AV 2 3d 2 0 AV 2 (B) d 3 0 AV 2 2 0 AV 2 (C) 2 d (D) 3d 7. The resistance of each straight section is r. Find the equivalent resistance between A and B. (A) 3 r (B) 3.5 r (C) 4 r (D) 4.5 r 8. PQ is an infinite current carrying conductor. AB and CD are smooth conducting rods on which a conductor EF moves with constant velocity V as shown. The force needed to maintain constant speed of EF is. 1   V  b 2   V  b 2 R (A)  0 𝑙n   (B)  0 𝑙n    VR  2  a     a  V   V  b 2 V R   V  b 2 (C)  0 𝑙n   (D)  0 𝑙n     2  a  R V    a  SECTION - II Multiple Correct Answers Type This section contains 4 Multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE may be correct. 9. Two capacitors C1 & C2 are charged to same potential V, but with opposite polarity as shown in fig. The switch S1 & S2 are then closed. (A) P.d. across two capacitors are same & is given by (C1  C2 )V (C1  C2 ) (B) P.d. across two capacitors are same & is given by C1V (C1  C2 )  (C  C ) 2 (C) Ratio of final energy to initial energy of the system is  1 2   (C1  C2 )   (C1)  (D) Ratio of final energy to initial energy of the system is  2    14. Satement-1 : A pendulum made of an insulated rigid massless rod of length 𝑙 is attached to a small sphere of mass m and charge q. The pendulum is undergoing oscillations of small amplitude having time period T. Now a uniform horizontal magnetic field B out of plane of page is switched on. As a result of this change, the time period of oscillations does not change. Satement-2 : A force acting along the string on the bob of a simple pendulum (such that tension in string is never zero) does not produce any restoring torque on the bob about the hinge. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True SECTION - IV Comprehension Type This section contains 1 Paragraphs. Based upon each paragraph, 3 Multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Paragraph for Question Nos. 15 to 17 In the shown circuit involving a resistor of resistance R , capacitor of capacitance C farad and an ideal cell of emf E volts, the capacitor is initially uncharged and the key is in position 1. At t = 0 second the key is pushed to position 2 for t0 = RC seconds and then key is pushed back to position 1 for t0 = RC seconds. This process is repeated again and again. Assume the time taken to push key from position 1 to 2 and vice versa to be negligible. 15. The charge on capacitor at t = 2RC second is 1 1  (A) CE (B) CE    e   1  1  1 1  1  (C) CE   e2  (D) CE   e e2  16. The current through the resistance at t = 1.5 RC seconds is (A) E e2R (1 1) e (B) E (1 1 ) eR e (C) E (1  1 ) (D) (1 1 ) R e e 20. In the circuit shown S1 and S2 are switches. S2 remains closed for a long time and S1 open. Now S1 is also closed. It is given that R = 10 , L = 1 mH and  = 3V. Just after S is closed, the magnitude of rate of change of current (in ampere/sec.) that is di , in the inductor L is x × 102 A/s find x dt x  A0  21. The equivalent capacitance between terminals ‘A’ and ‘B’ is 10   Find x. The letters have their usual  meaning. → 22. The current density J inside a long, solid, cylindrical wire of radius a = 12 mm is in the direction of the central axis and its magnitude varies linearly with radial distance r from the axis according to J = J0r , a where J0 = 105 4 A/m2. Find the magnitude of the magnetic field at r = a in µT. 2