Magnetics -05-SUBJECTIVE UNSOLVED LEVEL - I (C. B. S. E.)

(C. B. S. E.) SUBJECTIVE LEVEL - I (REVIEW YOUR CONCEPTS) 1. A circular coil of wire consisting of 100 turns. each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the center of the coil? 2. A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2.5m east of the wire. 3. A straight wire carrying a current of 12 A is bent into a semi-circular arc of radius 2.0cm as shown in Figure. What is the direction and magnitude of B at the centre of the arc? Would your answer be different if the wire were bent into a semi-circular arc of the same radius but in the opposite way as shown in figure. (a) (b) 4. A 3.0 cm wire carrying a current of 10A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the magnetic force on the wire ? 5. Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A. 6. A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and the normal to the plane of the coil makes an angle of 300 with the direction of a uniform horizontal magnetic field of magnitude 0.80 T. What is the magnitude of torque experienced by the coil ? 7. Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A; coil Y has 25 turns and caries a current 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre. 8. For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by, μ 0IR 2 N B  2x 2  R 2 3 2 (a) Show that this reduces to the familiar result for field at the centre of the coil. (b) Consider two parallel co-axial circular coils of equal radius R, and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R, and is given by, B  0.72 μ0 NI , approximately, R [Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.] 9. An electron emitted by a heated cathode and accelerated through a potential difference of 2.0 kV, enters a region with uniform magnetic field of 0.15 T. Determine the trajectory of the electron if the field (a) is transverse to its initial velocity, (b) makes an angle 300 with the initial velocity. 10. A magnetic field set up using Helmholtz coils (described in Exercise 5.19) is uniform in a small region and has a magnitude of 0.75 T. In the same region, a uniform electrostatic field is maintained in a direction normal to the common axis of the coils. A narrow beam of (single species) charged particles all accelerated through 15 kV enters this region in a direction perpendicular to both the axis of the coils and the electrostatic field. If the beam remains undeflected when the electrostatic field is 9.0 x 10-5 V m-1, make a simple guess as to what the beam contains. Why is the answer not unique ? 11. A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires. (a) What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero ? (b) What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field same as before ? (Ignore the mass of the wires.) g = 9.8 ms-2. 12. A uniform magnetic field of 1.5 T exists in a cylindrical region of radius 10.0 cm, its direction parallel to the axis along east to west. A wire carrying current of 7.0 A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if, (a) The wire intersects the axis (b) The wire is turned from N-S to northeast-northwest direction (c) The wire in the N-S direction is lowered from the axis by a distance of 6.0 cm ? 13. A uniform magnetic field of 3000 G is established along the positive z-direction. A rectangular loop of sides 10 cm and 5 cm carries a current of 12 A. What is the torque on the loop in the different cases shown in Fig. ? What is the force on each case ? Which case corresponds to stable equilibrium ? (a) (b) (c) (d) (e) (f) 14. A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the coil. If the current in the coil is 5.0 A, what is the (a) Total torque on the coil, (b) Total force on the coil, (c) Average force on each electron in the coil due to the magnetic field ? (The coil is made of copper wire of cross-sectional area 10-5 m2,and the free electron density in copper is given to be about 1029 m-3.) 15. A rectangular loop of sides 25 cm and 10 cm carrying current of 15 A is placed with its longer side parallel to a long straight conductor 2.0 cm apart carrying a current of 25 A. What is the net force on the loop ?