Title 12--magnetic-effect-of-current-.pdf ✅

Magnetic Effect of Current 1. A conductor of mass m and length l is placed perpendicular to a horizontal uniform magnetic field B. Suddenly a certain amount of charge is passed through it, and it is found to jump to a height h. The amount of charge that passes through the conductor is : (A) m√gh Bl (B) m√gh 2Bl (C) m√2gh Bl (D) None of these 2. The segment AB of wire carrying current I1 is placed perpendicular to a long straight wire carrying current I2 as shown in figure. The magnitude of force experienced by the straight wire AB is : (A) μ0I1I2 2π ln 3 (B) μ0I1I2 2π ln 2 (C) 2μ0I1I2 2π (D) μ0I1I2 2π 3. A tightly-wound long solenoid has n turns per unit length, radius r and carries a current i. A particle having charge q and mass m is projected from a point on the axis in the direction perpendicular to the axis. The maximum speed for which particle does not strike the solenoid will be : (A) μ0qrni 2m (B) μ0qrni m (C) 2μ0qrni 3m (D) None of these 4. If the acceleration and velocity of a charged particle moving in a constant magnetic region is given by a⃗ = a1iˆ + a2kˆ , v⃗ = b1iˆ + b2kˆ .[a1, a2, b1 and b2 are constants ], then choose the wrong statement : (A) Magnetic field may be along y-axis (B) a1b1 + a2b2 = 0 (C) Magnetic field is along x-axis (D) Kinetic energy of particle is always constant 5. A uniform solid non conducting sphere of radius R and total charge q rotates about its diametric axis with constant angular speed ω. The magnetic moment of the sphere is : (A) 1 3 qR 2ω (B) 2 3 qR 2ω (C) 1 5 qR 2ω (D) 2 5 qR 2ω 6. The magnetic field at the origin due to the current flowing in the wire as shown in figure below is : (A) − μ0I 8πa (iˆ + kˆ ) (B) μ0I 2πa (iˆ + kˆ ) (C) μ0I 8πa (−iˆ + kˆ ) (D) μ0I 4πa√2 (iˆ − kˆ ) 7. Two infinitely long linear conductors are arranged perpendicular to each other as shown in figure. If I1 = 2 A along the y-axis and I2 = 3 A along negative z axis and AP = AB = 1 cm, the value of magnetic field strength B⃗⃗ at P is :
(A) (3 × 10−5 T)jˆ + (−4 × 10−5 T)kˆ (B) (3 × 10−5 T)jˆ + (4 × 10−5 T)kˆ (C) (4 × 10−5 T)jˆ + (3 × 10−5 T)kˆ (D) (−3 × 10−5 T)jˆ + (4 × 10−5 T)kˆ 8. There exists a uniform magnetic and electric field each of magnitude 1 T and 1 V/m respectively along positive y-axis. A charged particle of mass 1 kg and of charge 1C is having velocity 1 m/sec along x-axis and is at origin at t = 0. Then the co- ordinate of particle at time π seconds will be: (A) (0,1,2) (B) (0, −π 2 /2, −2) (C) (2, π 2 /2,2) (D) (0, π 2 /2,2) 9. A current carrying loop is placed in a uniform magnetic field pointing in negative z direction. Branch PQRS is a three quarter circle, while branch PS is straight. If force on branch PS is F, force on branch PQR is : (A) √2F (B) F √2 (C) πF √2 (D) √2πF 10. A particle of mass m and positive charge q enters a region of magnetic field with speed v. There is a region in which the magnetic field is absent, as shown. The particle after entering the region collides elastically with a rigid wall. Time after which the velocity of particle becomes anti-parallel to its initial velocity is : (A) m 2qB (π + 4) (B) m qB (π + 2) (C) m 4qB (π + 4) (D) m 4qB (2π + 3) 11. A particle (mass m and charge q ) is at rest at origin. An electric field E⃗⃗ = 10kˆ units and magnetic field B⃗⃗ = −8iˆ + 6jˆ units is switched on in the region. Speed of the particle as function of its z- coordinate is : (A) √ 10qz m (B) √ 20qz m (C) √ 30qz m (D) √ 40qz m 12. A metallic rod PQ is hinged at point P and it can rotate about point P in vertical plane as shown in the figure. If mass of rod is m and length l, then the current in PQ, such that it remains in equilibrium as shown is : (Separation between P and current currying conductor AB is very small) (A) 2mgπ μ0i1 (B) mgπ 2μ0i1
(C) mgπ 4μ0i1 (D) mgπ μ0i1 13. Figure shows a spiral path of a particle which has entered a resistive medium where a uniform magnetic field acts perpendicular to the plane and into the plane of the spiral. Then the particle is : (A) positively charged and entering at P (B) positively charged and entering at Q (C) negatively charged and entering at P ⊗ B (D) negatively charged and entering at Q 14. A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One of the arcs AB of the ring subtends an angle θ at the centre. The value of the magnetic induction at the centre due to the current in the ring is : (A) zero, only if θ = 180∘ (B) zero for all values of θ (C) proportional to 2(180∘ − θ) (D) inversely proportional to r 15. The magnetic induction in vacuum at the centre of any square coil (of one turn) of side ' a ' and carrying a current I is kI/a where k is independent. The magnitude of the induction at X, Y, Z are B1, B2 and B3 respectively. Then : (A) B3 > B1 > B2 (B) B2 > B3 > B1 (C) B2 > B1 > B3 (D) B1 > B2 > B3 MULTIPLE CORRECT ANSWERS TYPEEach of the following Question has 4 choices A, B, C & D, out of which ONE or MORE Choices may be Correct: 16. When a current carrying coil is placed in a uniform magnetic field with its magnetic moment anti- parallel to the field, then : (A) torque on it is maximum (B) torque on it is zero (C) potential energy is maximum (D) dipole is in unstable equilibrium 17. If a long cylindrical conductor caries a steady current parallel to its length, then : (A) the electric field along the axis is zero (B) the magnetic field along the axis is zero (C) the magnetic field outside the conductor is zero (D) the electric field outside the conductor is zero 18. An infinitely long straight wire is carrying a current I1. Adjacent to it there is another equilateral triangular wire having current I2. Choose the wrong options. (A) Net force on loop is leftwards (B) Net force on loop is rightwards (C) net force on loop is upwards (D) net force on loop is downwards 19. A charged particle revolves in circular path in uniform magnetic field after accelerating by a potential difference of V volts. Choose the correct options if V is doubled. (A) kinetic energy of particle will become two times (B) radius in circular path will become two times (C) radius in circular path will become √2 times (D) angular velocity will remain unchanged 20. A long thick conducting cylinder of radius R carries a current uniformly distributed over its cross section. Choose correct options. (A) The magnetic field strength is maximum on the surface (B) The magnetic field strength is zero on the surface (C) The strength of the magnetic field inside the cylinder will vary as inversely proportional to r, where r is the distance from the axis. (D) The energy density of the magnetic field outside the conductor varies as inversely proportional to r 2 , where ' r ' is the distance from the axis. 21. A nonconducting disc having uniform positive charge Q, is rotating about its axis in anticlock wise direction with uniform angular velocity ω. The
magnetic field at the centre of the disc is : (A) directed outward (B) having magnitude μ0Qω 4πR (C) directed inwards (D) having magnitude μ0Qω 2πR 22. A charged particle of charge q, mass m is moving with initial velocity ' v ' as shown in figure in a uniform magnetic field B kˆ . Select the correct alternative/alternatives. (A) velocity of particle when it comes out from magnetic field is v⃗⃗ = vcos 60∘ iˆ + vsin 60∘ jˆ (B) time for which the particle was in magnetic field is (C) distance travelled in magnetic field is πm V 3qB πm 3qB (D) the particle will never come out of magnetic field 23. A particle of charge ' q ' & mass ' m ' enters normally (at point P ) in a region of magnetic field with speed v. It comes out normally from Q after time T as shown in figure. The magnetic field B is present only in the region of radius R and is constant and uniform. Initial and final velocities are along radial direction and they are perpendicular to each other. For this to happen, which of the following expression(s) is(are) correct ? (A) B = mv qR (B) T = πR 2v (C) T = πm 2q B (D) None of these 24. From a cylinder of radius R, a cylinder of radius R/2 is removed, as shown. Current flowing in the remaining cylinder is I. Magnetic field strength is: (A) zero at point A (B) zero at point B (C) μ0I 3πR at point A (D) μ0I 3πR at point B 25. Consider three quantities x = E B , y = √1/μ0ε0 and z = l CR . Here, l is length of a wire, C is a capacitance and R is a resistance. All other symbols have standard meanings. (A) x, y have the same dimensions (B) y, z have the same dimensions (C) z, x have the same dimensions (D) none of the three pairs have the same dimensions 26. A conductor ABCDE, shaped as shown, carries current I. It is placed in the x-y plane with the ends A and E on the x-axis. A uniform magnetic field of magnitude B exists in the region. The force acting