Magnetics -04-OBJECTIVE UNSOLVED LEVEL - I

OBJECTIVE UNSOLVED LEVEL - I 1. 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) μ0 NI b μ 0 NI b (b) 2μ0 NI a μ0 IN b (c) 2b  aln a (d) b  a  ln a . 2. Two particles A and B of masses mA and mB respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are vA and vB respectively and the trajectories are as shown in the figure then (a) mAvA < mBvB (b) mAvA > mBvB (c) mA < mB and vA < vB (d) mA = mB and vA = vB. 3. An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the +x direction and a magnetic field along the +z direction, then (a) positive ions deflect towards +y direction and negative ions towards -y direction (b) all ions deflect towards +y direction (c) all ions deflect towards -y direction (d) positive ions deflect towards -y direction and negative ions towards +y direction. 4. An infinitely long conductor PQR is bent to form a right angle as shown. A current I flows through PQR. The magnetic field due to this current at the point M is H1. Now another infinitely long straight conductor QS is connected at Q so that the current is I/2 in QR as well as in QS, the current in PQ remaining unchanged. The mag- netic field at M is now H2. The ratio H1/H2 is given by: (a) 1/2 (b) 1 (c) 2/3 (d) 2. - P I 900 Q M 900 S + R - 5. A circular loop of radius R, carrying current I, lies in xy plane with its centre at origin. The total magnetic flux through xy plane is: (a) directly proportional to I (b) directly proportional to R (c) inversely proportional to R (d) zero. 6. A particle is moves in a circular path of diameter 1.0 m under the action of magnetic field of 0.40 Tesla. An electric field of 200 V/m makes the path of particle straight. Find the charge / mass ratio of the particle (a) (c) 2.5 105 C/kg 3.5 105 C/kg (b) (d) 2 105 C/kg 3 105 C/kg . 7. A charged particle is released from rest in a region of steady and uniform electric and magnetic fields which are parallel to each other. The particle will move in a (a) straight line (b) circle (c) helix (d) cycloid. 8. A proton, a deutron and an α -particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If rP, rd and r α denote respectively the radii of the trajec- tories of these particles then (a) (c) rα  rp  rd rα  rd  rp (b) (d) rα  rd  rp rp  rd  rα . 9. Two thin long parallel wires separated by a distance b are carrying a current i amp. each. The magnitude of the force per unit length exerted by one wire on the other is (a) μ0i2 b2 (b) 2 0 2πb (c) μ0i (d) 2πb μ0i . πb2 10. A charged particle of mass m and charge q enters a magnetic field B with a velocity v at an angle θ with the direction of B. The radius of the resulting path is (a) (c) mv sin θ q B mv q B (b) (d) mv q Bsin θ mv tanθ q B . 11. An electron falling freely under gravity enters a region of uniform horizontal magnetic field pointing north to south. The particle will be deflected towards (a) east (b) west (c) north (d) south. 12. A uniform magnetic field of magnitude 0.20 T exists in space from east to west. With what speed should a particle of mass 0.010 g and having a charge 1.0 105 C so that it moves with a uniform velocity (a) 48 m/s (b) 49 m/s (c) 47 m/s (d) 50 m/s be projected from south to north 13. In a region of space uniform electric field is present as E  E ˆj and uniform magnetic field is present as B  B .kˆ . An electron is released from rest at origin. Which of the following best represents the path followed by electron after release. y y (a) (b) x x y y (c) (d) x Z 14. The negatively charged disc in figure is rotated clock-wise. What is the direction of the magnetic field at point A in the plane of the disc? A (a) Into the page (b) Out of the page (c) Up the page (d) Down the page. 15. Which of the following particle will have minimum frequency of revolution when projected with the same velocity perpendicular to a magnetic field? (a) electron (b) proton (c) He+ (d) Li+. OBJECTIVE UNSOLVED LEVEL - II 1. A particle of mass m and charge q moves with a constant velocity v along the positive x-direction. It enters a region containing a uniform magnetic field B directed along the negative z direction, extending from x = a to x = b. The minimum value of v required so that the particle can just enter the region x > b is (a) qb B/m (b) q (b-a)B/m (c) qa B/m (d) q(b+a) B/2m. 2. A long straight wire along the z-axis carries a current I in the negative z direction. The magnetic vector field B at a point having coordintes (x, y) in the z = 0 plane is: (a) (c) 0I(yiˆ  xˆj) 2(x2  y2 ) 0I(xˆj  yiˆ) 2(x2  y2 ) (b) (d) 0 I(yˆi  xˆj) 2(x2  y2 ) 0 I(xˆj  yˆi) 2(x2  y2 ) . z 3. A non-planar loop of conducting wire carrying a current I is placed y as shown in the figure. Each of the straight sections of the loop is of length 2a. The magnetic filed due to this loop at the point P (a, 0, a) points in the direction. x (a) (c) (ˆj  kˆ) (iˆ  ˆj  kˆ) (b) (d) (ˆj  kˆ  ˆi) 2a (ˆi  kˆ) . 4. A long, straight wire carries a current along the Z-axis. One can find two points in the X-Y plane such that (a) the magnetic fields are equal (b) the directions of the magnetic fields are the same (c) the magnitudes of the magnetic fields are equal (d) the field at one point is opposite to that at the other point. 5. In a coaxial, straight cable, the central conductor and the outer conductor carrry equal currents in opposite directions. The magnetic field is zero. (a) outside the cable (b) inside the inner conductor (c) inside the outer conductor (d) in between the two conductors. 6. Two parallel, long wires carry currents i1 and i2 with i1 > i2. When the currents are in the same direction, the magnetic field at a point midway between the wires is 90 reversed, the field becomes 30T . The ratio i1 / i2 is (a) 4 (b) 3 (c) 2 (d) 1. μT . If the direction of is 7. Two long parallel wires are at a distane 2d apart. They carry steady equal currents flowing out of the plane of the paper, as shown. The variation of the magnetic field B along the line XX' is given by : x (a) x' x x' (b) x (c) x x' x' (d) . 8. Two insulated rings, one of slightly smaller diameter than the other, are suspended along their common diameter as shown. Initially the planes of the rings are mutually perpendicular. When a steady cur- rent is set up in each of them. (a) the two rings rotate into a common plane (b) the inner ring oscillates about its initial position (c) the outer ring stays stationary while the inner one moves into the plane of the outer ring (d) the inner ring stays stationary while the outer one moves into the plane of the inner ring. 9. A charged particle goes undeflected in a region containing electric and magnetic field. It is possible that → → → → → → (a) E||B, v || E (b) E is not parallel to B → → → → → → → (c) v||B but E is not parallel to B (d) E || B but v is not parallel to E . 10. A particle is projected in a plane perpendicular to a uniform magnetic field. The area bounded by the path described by the particle is proportional to (a) the velocity (b) the momentum (c) the kinetic energy (d) none of these. 11. The magnetic field at the origin due to a current element idl placed at a position r is  i dl  →  i →  dl (a) 0 r 4 r3 (b)  0 r 4 r3  i →  dl  i dl  → (c) 0 r 4 r3 (d)  0 r . 4 r3 12. A proton of mass 1.67 × 10-27 kg and charge 1.6 × 10-19 C is projected with a speed of 2 × 106 m/s at an angle of 600 to the X-axis in XY plane. If a uniform magnetic field of 0.104 tesla is applied along the Y-axis, the path of the proton is (a) a circle of radius  0.1 m and time period 107 s (b) a circle of radius  0.2 m and time period π 107 s (c) a helix of radius  0.1 m and time period 2π 107 s (d) a helix of radius  0.2 m and time period 4π 107 s . 13. A potential difference of 500 V is applied across a parallel plate capacitor. The separation be- tween the plates is 2×10-3 m. The plates of the capacitor are vertical. An electron is projected vertically upwards between the plates with a velocity of 105 m/s and it moves undeflected between the plates. The magnetic field acting perpendicular to the electric field has magnitude of (a) 0 Wb/m2 (b) 2.5 Wb/m2 (c) 3.0 Wb/m2 (d) 5.0 Wb/m2. 14. Two similar coaxial coils, separated by some distance, carry the same current I but in opposite directions. The magnitude of the magnetic field B at a point on the axis at the mid point of the line joining the centre is : (a) zero (b) the same as that produced by one coil (c) twice that produced by one coil (d) half of that produced by one coil. 15. Conductor ABC consist of two quarter circular path of radius R lies in X-Y plane and carries current I as shown. A uniform mag- netic field → is switched on in the region that exert force → = IRB ˆ on conductor ABC. → can be F (a) 0 k B0 ( ˆi ) B (b) B0 iˆ (c) B0 (ˆi  ˆj) (d) both (b) and (c).