Free Ncert Solutions for 12th Class Physics Electro Magnetic Induction - Studyadda.com

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12th Physics Electro Magnetic Induction

1)

Predict the direction of induced current in the situations described by the following Fig. 2(a) to (f).
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2)

Use Lenz's law to determine the direction of induced current in the situations describe by Figure: (a) A wire of irregular shape turning into a circular shape (b) A circular loop being deformed into narrow straight wire.
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3)

A long solenoid with 15 turns per cm has a small loop of area placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced e.m.f. in the loop while the current is changing?
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4)

A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the e.m.f. developed across the cut if the velocity of the loop is in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case?
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5)

A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the e.m.f. developed between the centre and the ring.
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6)

A circular coil of radius 8.0 cm and 20 turns rotates about its vertical diameter with an angular speed of 500 rad in a uniform horizontal magnetic field of magnitude . Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance 10 , calculate the maximum value of current in the coil. Calculate the average power loss due to Joule beating. Where does this power come from?
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7)

A horizontal straight wire 10 m long extending from east to west is falling with a speed of , at right angles to the horizontal component of the earth's magnetic field, . (a) What is the instantaneous value of the e.m.f. induced in the wire? (b) What is the direction of the e.m.f.? (c) Which end of the wire is at the higher electrical potential?
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8)

Current in a circuit falls from 5.0 A to 0.0 A s. If an average end of 200 V induced, give an estimate of the self-inductance of the circuit.
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9)

A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil?
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10)

A jet plane is travelling towards west at a speed of 1800 km/h. What is the voltage difference developed between the ends of the wing having a span of 25 m, if the Earth magnetic field at the location has a magnitude of and the dip angle is ?
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11)

Suppose the loop in Exercise 6.4 is stationer, but the current feeding the electromagnet that produces the magnetic field is gradually reduced so that the field decreases from its initial value of 0.3 T at the rate of 0.02 T . If the cut is joined and the loop has a resistance of 1.6, how much power dissipated by the loop as heat? What is the source of this power?
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12)

A square loop of side 12 cm with its side parallel to and axes is moved with velocity of in the positive direction in an environment containing magnetic field in the positive z-direction. The field is neither uniform in space nor constant in time. It has a gradient of along the negative x-direction (that is increases by as one moves the negative x-direction), and it is decreasing in time at the rate of . Determine the direction and magnitude of the induced current the loop if its resistance is .
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13)

It is desired to measure the magnitude of field between the poles of a powerful loud speaker magnet. A small flat search coil of area with 25 closely would turns, is positioned normal to the field direction, and then quickly snatched out of the field region. Equivalently, one can give it a quick turn to bring its plane parallel to the field direction. The total charge flown in the coil (measured by a ballistic galvanometer connected to coil) is 7.5 mC. The combined resistance of he coil and the galvanometer is . Estimate the field strength of magnet.
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14)

Figure shows a metal rod PQ resting on the rails AB and positioned between the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three mutual perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod = 15 cm, B = 0.50 T,resistance of the closed loop containing the rod = 9.0 m . Assume the field to be uniform. (a) Suppose K is open and the rod is moved with a speed of 12 cm in the direction shown. Give the polarity and magnitude of the induced emf. (b) Is there an excess charge built up at the ends of the rods when K is open? What if K is closed? (c) With K open and the rod moving uniformly, there is no net force on the electrons in the rod PQ even though they do experience magnetic force due to the motion of the rod. Explain. (d) What is the retarding force on the rod when K is closed? (e) How much power is required (by an external agent) to keep the rod moving at the same speed when K is closed? How much power is required when K is open? (f) How much power is dissipated as heat in the closed circuit? What is the source of this power? (g) What is the induced emf in the moving rod if the magnetic field is parallel to the rails instead of being perpendicular?
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15)

An air-cored solenoid with length 30 cm, area of cross-section and number of turns 500, carries a current of 2.5 A. The current is suddenly switched off in a brief time of . How much is the average back emf induced across the ends of the open switch in the circuit? Ignore the variation in magnetic field near the ends of the solenoid.
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16)

(a) Obtain an expression for the mutual inductance between a long straight wire and a square loop of side a as shown in Figure. (b) Now assume that the straight wire carries a current of 50 A and the loop is moved the right with a constant velocity, = 10 m/s. Calculate the induced e.m.f. in loop at the instant when = 0.2 m. Take = 0.1 m and assume that the loop has j large resistance.
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17)

The line charge per unit length is lodged uniformly onto the rim of a wheel of mass M and radius R. The wheel has light non-conducting spokes and is free to rotate without friction about its axis (Figure). A uniform magnetic field extends over a circular magnetic field extends over a circular region within the rim. It given by = 0 [otherwise] What is the angular velocity of the wheel after the field is suddenly switched off?
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18) A square of side L meters lies in the x-y plane in a region, where the magnetic field is given by , where is constant. The magnitude of flux passing through the square is (a) (b) (c) (d)
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19) A loop, made of straight edges has six corners at A (0, 0, 0), B (L, O, 0), C (L, L, 0), D (0, L, 0), E (0, L, L) and F (0, 0, L). A magnetic field is present in the region. The flux passing through the loop ABCDEFA (in that order) is (a) (b) (c) (d)
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20) A cylindrical bar magnet is rotated about its axis. Fig. 4(EP).1. A wire is connected from the axis and is made to touch the cylindrical surface through a contact. Then (a) a direct current flows in the ammeter A (b) no current flows through the ammeter A (c) an alternating sinusoidal current flows through the ammeter A with a time period (d) a time varying non-sinosoidal current flows through the ammeter A
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21) There are two coils A and B as shown in Fig. 4(EP).2. A current starts flowing in B as shown, when A is moved towards B and stops when A stops moving. The current in A is counter- clockwise. B is kept stationary when A moves. We can infer that (a) there is a constant current in the clockwise direction in A (b) there is a varying current in A (c) there is no current in A (d) there is a constant current in the counter- clockwise direction in A
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22) Same as problem 4 except the coil A is made to rotate about a vertical axis, Fig. 4(EP).3. No current flows in B it A is at rest. The current in coil A, when the current in B (at t = 0) is counterclockwise and the coil A is as shown at this istant, t = 0, is (a) constant current clockwise (b) varying current clockwise (c) varying current counterclockwise (d) constant current counterclockwise
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23) The self inductance L of a solenoid of length and area of cross-section A, with a fixed number of turns N increases as (a) and A increase (b) decreases and A increases (c) increases and A decreases (d) both and A decrease
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24) A metal plate is getting heated. It can be because (a) a direct current is passing through the plate (b) it is placed in a time varying magnetic field (c) it is placed in a space varying magnetic field, but does not vary with time (d) a current (either direct or alternating) is passing through the plate
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25) An e.m.f. is produced in a coil, which is not connected to an external voltage source. This can be due to (a) the coil being in a time varying magnetic field (b) the coil moving in a time varying magnetic field (c) the coil moving in a constant magnetic field (d) the coil is stationary in external spatially varying magnetic field, which does not change with time
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26) The mutual inductance of coil 1 with respect to coil 2 (a) increases when they are brought nearer (b) depends on the current passing through the coils (c) increases when one of them is rotated about an axis (d) is the same as of coil 2 with respect to coil 1
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27) A circular coil expands radially in a region of magnetic field and no electromotive force is produced in the coil. This can be because (a) the magnetic field is constant (b) the magnetic field is in the same plane as the circular coil and it may or may not vary (c) the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably (d) there is a constant magnetic field in the perpendicular (to the plane of the coil) direction
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28) Consider a magnet surrounded by a wire with an on/off switch S, Fig. 4(EP).5. If the switch is thrown from the off position (open circuit) to the on position (closed circuit), will a current flow in the circuit? Explain.
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29) A wire in the form of a tightly wound solenoid is connected to a DC source, and carries a current. If the coil is stretched so that there are gaps between successive elements of the spiral coil, will the current increase or decrease? Explain.
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30) A solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, will the current increase or decrease? Explain.
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31) Consider a metal ring kept on top of a fixed solenoid (say on a cardboard), Fig. 4(EP).6. The centre of the ring coincides with the axis of the solenoid. If the current is suddenly switched on, the metal ring jumps up. Explain.
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32) Consider a metal ring kept (supported by a cardboard) on top of a fixed solenoid carrying a current , Fig. 4(EP).6. The centre of the ring coincides with the axis of the solenoid. If the current in the solenoid is switched off, what will happen to the ring?
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33) Consider a metallic pipe with an inner radius of 1 cm. If a cylindrical bar magnet of radiuscm is dropped through the pipe, it takes more time to come down than it takes for a similar unmagnetised cylindrical iron bar dropped through the metallic pipe. Explain.
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34) A magnetic field in a certain region is given by and a coil of radius with resistance R is placed in the x-y plane with its centre at the origin in the magnetic field, Fig. 4(EP).7. Find the magnitude and the direction of the current at (, 0, 0) at and
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35) Consider a closed loop C in a magnetic field, Fig. 4(EP).8. The flux passing through the loop is defined by choosing a surface whose edge coincides with the loop and using the formula ..... Now if we chose two different surfacesand having C as their edge, would we get the same answer for flux. Justify your answer.
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36) Find the current in the wire PQ for the configuration shown in Fig. 4(EP).9. Wire PQ has negligible resistance. B, the magnetic field is coming out of the paper. is a fixed angle made by PQ travelling smoothly over two conducting parallel wires separated by a distance d.
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37) A (current vs time) graph of the current passing through a solenoid is shown in Fig. 4(EP).10. For which time is the back electromotive force a maximum? If the back emf at t = 3 s is e, find the back emf at t = 7 s, 15 s and 40 s. OA, AB and BC are straight line segments.
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38) There are two coils A and B separated by some distance. If a current of 2 A flows through A, a magnetic flux of Wb passes through B (no current through B). If no current passes through A and a current of 1 A passes through B, what is the flux through A?
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39) A magnetic field covers a large region where a wire AB slides smoothly over two parallel conductors separated by a distance d, Fig. 4(EP).11. The wires are in the x-y plane. The wire AB (of length d) has resistance R and the parallel wires have negligible resistance. If AB is moving with velocity , what is the current in the circuit? What is the force needed to keep the wire moving at constant velocity?
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40) A conducting wire XY of mass m and negligible resistance slides smoothly on two parallel conducting wires as shown in Fig. 4(EP).12. The closed circuit has a resistance R due to AC. AB and CD are perfect conductors. There is a magnetic field B =. (i) Write down equation for the acceleration of the wire XY. (ii) If B is independent of time, obtain (t), assuming (0) = . (iii) For (b), show that the decrease in kinetic energy of XY equals the heat lost in R.
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41) ODBAC is a fixed rectangular conductor of negligible resistance (CO is not connected) and OP is a conductor which rotates clockwise with an angular velocity , Fig. 4(EP).13. The entire system is in a uniform magnetic field B whose direction is along the normal to the surface of the rectangular conductor ABDC. The conductor OP is in electric contact with ABDC. The rotating conductor has a resistance of per unit length. Find the current in the rotating conductor, as it rotates by 180.
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42) Consider an infinitely long wire carrying a current (t), with = constant. Find the current produced in the rectangular loop of wire ABCD if its resistance is R, Fig. 4(EP).17.
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43) A rectangular loop of wire ABCD is kept close to an infinitely long wire carrying a current for and for t > T, Fig. 4(EP).18. Find the total charge passing through a given point in the loop, in time . The resistance of the loop is R.
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44) A magnetic field B is confined to a region r a and points out of the paper (the z-axis), r = 0 being the centre of the circular region. A charged ring (charge = Q) of radius b, b > a and mass m lies in the x-y plane with its centre at the origin. The ring is free to rotate and is at rest. The magnetic field is brought to zero in time . Find the angular velocity of the ring after the field vanishes.
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45) A rod of mass m and resistance R slides smoothly over two parallel perfectly conducting wires kept sloping at an angle with respect to the horizontal, Fig. 4(EP).19. The circuit is closed through a perfect conductor at the top. There is a constant magnetic field B along the vertical direction. If the rod is initially at rest, find the velocity of the rod as a function of time.
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46) Find the current in the sliding rod AB (resistance = R) for the arrangement shown in Fig. 4(EP).20. B is constant and is out of the paper. Parallel wires have no resistance. is constant. Switch S is closed at time t = 0.
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47) Find the current in the sliding rod AB (resistance = R) for the arrangement shown in Fig. 4(EP).21. B is constant and is out of the paper. Parallel wires have no resistance, is constant. Switch S is closed at time t = 0.
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48) A metallic ring of mass m and radius (ring being horizontal) is falling under gravity in a region having a magnetic field. If z is the vertical direction, the z-component of magnetic field is . If R is the resistance of the ring and if the ring falls with a velocity , find the energy lost in the resistance. If the ring has reached a constant velocity, use the conservation of energy to determine in terms of m, B, and acceleration due to gravity g.
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49) A long solenoid 'S' has ?n? turns per meter, with diameter ''. At the centre of this coil, we place a smaller coil of 'N ' turns and diameter 'b' (where b < a). If the current in the solenoid increases linearly with time, what is the induced emf appearing in the smaller coil. Plot graph showing nature of variation in emf, if current varies as a function of
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