Electromagnetic Induction Questions and Answers

16 In the circuit shown E 18 kV C 10 F R 4 M2 R 6M2 R 3 MQ With C completely uncharged switch S is suddenly closed at t 0 1 1 E R www S 11 www R2 12 www R 3 C 13 a Determine the current through each resistor for t 0 and t b What are the values of V potential difference across R at t 0 and t 2 c Plot a graph of the potential difference V versus t and determine the instantaneous value of V 07 as a function the capacitor as itor

A circular flat coil with a 2 50 cm radius sits in a horizontal plane There is a vertical time varying magnetic field B t that induces an emf of magnitude 195 mV at the instant when the magnetic field is changing at a rate of 0 850 T s How many turns does the coil have 117 414 367 29 2 84 4

The atomic mass of 2Th is 234 04359 u and that of 23 Pa is 234 04330 u The energy released in the reaction 234 Th 234 Pa will be 0 27 MeV 0 54 MeV 0 12 MeV 07 May

A rectangular loop with a sliding connector of length 1 0 field B m is situated in a uniform magnetic 2T perpendicular to the plane of loop Resistance of connector is r 20 Two resistance of 60 and 30 are connected as shown in figure The external force required to keep the connector moving with a constant velocity v 2m s is 1 2 Question Type Single Correct Type C 6 N 4 N www 2 N 69 B 3Q

7 A very long metallic hollow pipe of length 1 and radius r I is carrying charge Q uniformly distributed upon it The pipe is rotated about its axis with constant angular speed c The energy stored in the pipe of length is 100 H Q w r 800ml 4 0 00 7 H Q w r H Q w r 1 2 3 4 100zl 200ml 400zl 8 A current of 1A is flowing through a straight conductor of length 16 cm The magnetic induction in tesla at a point 10 cm from the either end of the wire is

In a decaying L R circuit the time after which energy stored in the inductor reduces to one fourth of its intitial value is En2 R 1 ln 3 2 R L 45 4 R 2 0 5 4 1 2 1

A long solenoid of the cross sectional radius R has a thin insulated wire ring tightly put on its winding One half of the ring has the resistance 10 times that of the other half The magnetic induction produced by the solenoid varies with time as B bt whose b is a constant If the magnitude of the electric field strength in the ring is Rb 9 where p and q are the smallest positive integers then what is the value of p q

17 In a series circuit C 2 F L 1mH and R 100 When the current in the circuit is maximum at that time the ratio of the energies stored in the capacitor and the inductor will be b 1 2 d 1 5 c21 an ac circuit peak value of voltage is 423 volts Its effective voltage is 48

1 A uniform rod of mass m is moving with constant velocity v in a perpendicular uniform magnetic field B as shown The resistance of rod is r The current flowing through rod R and R will be R 6r x 1 2 x xx x 3 X X X X X X X X Bv L X X X X X X X X X X 3r 3 3r V 2 BvL 1 Bv L 3 3r Bv L 1 BvL 2 Bv L 3 3r 3 3r 3 3r BvL 1 BvL 1 BvL 3r 3 3r X X X X X X XXX X R 3 r

A magnetic field B Bosin wt k covers a large region where a wire AB slides smoothly over two parallel conductors separated by a distance d Fig 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 v what is the current in the circuit What is the force needed to keep the wire moving at constant velocity faq bosil C A E BIL e sunt 1

In the circuit shown below switch S is kept open and circuit is in steady state At t 0 the switch S is closed and new steady state is reached after some time Mark the CORRECT option s 100 F 392 6V www 302 eeeeeee www 500mH 30 S 12V A Current in the inductor when the circuit reaches the new steady state is 4A B The net change in flux in the inductor is 1 5 Wb C The potential difference across the inductor is 9 V when the circuit reaches a new steady state D The charge stored in the capacitor in the new steady state is 1 2 mC

A copper ring is placed co axially in a time varying cylindrically symmetric magnetic field given by B btk Radius of ring is r Resistance of one half of the ring is double that of remaining half The magnitude of the electric field conservative inside the copper br Find K b K ring is E 42 Art

A single phase transformer is connected to a 230 volt 50Hz supply The net cross sectional area of the core is 60 mm The number of turns of the primary is 500 And in secondary 100 Determine a Transformation ration b EMF in the secondary

One solenoid is centered inside another The outer one has a length of 50 0 cm and contains 6750 coils while the coaxial inner solenoid is 3 0 cm long and cm in area and contains 150 coils The current in the outer solenoid is changing at 3000 A s Find the emf induced in V in the inner solenoid Round off to nearest integer

When north pole of a magnet is moved to the plane of the coil as shown perpendicular in figure then Induced Current NAN A B Capacitor S a emf is induced b Induced current flows from B to A along the coil when A and B are connected through resistor c Electrons flow from A to B along the coil d Hence plate A will become positively charged

In the given branch PQ of a circuit shown in figure a current i 5t 5 A is flowing where t is in second The potential difference between points P and Q Vp Vo at t 1 s is 10 V Q 15 V 15 V 12 V mmm L 1 Hi R 292 P

A solenoid has an inductance of 5 H and a resistance of 1 0 Q connected to a battery of emf 10 V The time taken for the magnetic energy to reach of its maximum value is approximately 1 8 s 2 7 S 3 5 s 4 2 S

Wire 1 is now removed and Wire 2 is exposed to a magnetic field of strength 73 mT such that the magnetic field lines make an angle to the wire as shown in Figure Q3c The current in Wire 2 has the same magnitude as in b and flows downwards Wire 2 experiences a magnetic force of magnitude 859 uN c Determine the direction of this magnetic force stating the name of the rule which you use to determine this and calculate Figure Q3c Orientation of magnetic field lines around Wire 2 The current supplied to Wire 2 is now switched off It is placed in a region of magnetic field strength 415 mT where the wire can be moved at a constant speed v in the horizontal plane either to the left or to the right as shown in Figure Q4d During this process an emf of 0 10 V is induced across the ends of the wire and the top end of the wire acquires a positive charge d Calculate the velocity of the wire including a direction and state the rule used to determine this direction B H 3 3

A coil of inductance L and zero resistance is connected to a source of variable emf at t 0 The emf of the source is varied with time according to the graph shown on the right above What will be the average current that flows through the coil during time T A VT 2L A B VT 3L T C 3V T 2L D VT L eing at a rate of 4 A s through a coil of inductance

5 A long straight wire carries a steady current I and a metal bar with length I is moving at a constant velocity v as shown in figure Point a is at a distance d from the wire i Calculate the emf induced in the bar ii Which point a orb is at higher potential iii If the bar is replaced by a rectangular wire loop of resistance R what is the magnitude of the current induced in the loop d a b V I d W V

is kept rotating with a constant angular speed w in a vertical plane about a horizontal axis at the end O The free end A is arranged to slide without friction along a fixed conducting circular ring in the same plane as that of rotation A uniform and constant magnetic induction B is applied perpendicular and into the plane of rotation as shown in figure An inductor L and an external resistance R are connected through a switch S between the point O and a point on the ring to form an electrical circuit Neglect the resistance of the ring and the rod Initially the switch is open What is the induced emf across the terminals of the switch i Obtain an expression for the current as a function of time after switch S is closed ii Obtain the time dependence of the

6 ELECTROMAGNETIC INDUCTION The directions of induced current in coil for different kinds of motion of magnets a S S b S N c N N Clockwise induced current S Clockwise induced current s No S No induced current because there is no change of flux linked with

In the circuit shown in Fig The capacitor has capacitance C 20 F and is initially charged to 100 V with the polarity shown The resistor Ro has resistance 100 at time t 0 the switch is closed The smaller circuit is not connected in any way to the larger one The wire of the smaller circuit is not connected in any way to the larger one The wire of the smaller circuit has a resistance of 1 0wm and contains 25 loops The larger circuit is rectangle 2 0 m by 4 0 m while the smaller one has dimensions a 10 0 cm and b 20 0 cm The distance c is 5 0 cm The figure is not drawn to scale Both circuits are held stationary Assume that only wire nearest to the smaller circuit produces an appreciable magnetic field through it The current in the larger circuit 200ms

A student constructs an inductor shown in Figure Q1a by winding an insulated metal wire around a core of soft magnetic material ferrite The cylindrical coil has 9 turns a length of 458 mm and a diameter of 16 mm The core has a relative permeability of 325 and negligible resistance End Y End X End P 17 End Q Figure Q1a A cylindrical coil inductor resistor At t 0 s the student completes a series circuit by connecting end X of the wire to the positive terminal of a power supply and end Y to a 10 that was connected to the negative terminal of the supply The power supply has an emf of 12 V and a negligible internal resistance a i Show that the inductance of this inductor is approximately 15 H Calculate the time constant of this LR circuit ii iii Calculate the current in the circuit at time t 3 us Calculate the time taken for the current in the circuit to reach 1 1 A The student leaves the inductor connected to the power supply until the current reaches a steady value b i i ii iii Calculate the magnitude of the magnetic field strength inside the inductor Which end P or Q of the inductor is the North pole State the name of the rule you have used to determine this How much magnetic flux is coming out of the North pole of the inductor Calculate the amount of energy stored within the magnetic field of the inductor

When a magnet is allowed to fall through two identical metal coils at different temperatures then magnet falls slowly through the coil at low temperature as its resistance is less more induced current flows so more is the opposition A magnet all 50

Imagine a cone of height h and radius R placed in a uniform electric field E parallel to its axis What is the ratio of electric flux through the flat surface of the cone and the curved surface of the cone 1 2 2 3 3 1 for 4

Zero An infinitely long wire carries current i along z axis Find flux through the right angled isosceles trangular region coplanar with the wire as shown in figure id xid xy loo 93 47 14 E OF X 2 Jw 2 10 a a a C BA Su through the hemispherical surface

disc of radius r is made of a material of negligible resistance and can rotate about a conducting horizontal shaft A smaller non conducting disc of radius a is fixed onto the same shaft and has a massless cord wrapped around it which is attached to a small object of mass m as shown Two ends of a resistor of resistance R are connected to the perimeter of the disc and to the shaft by sliding contacts The system is then placed into a uniform horizontal magnetic field B and the mass m is released Find the terminal angular velocity with which the disc will rotate finally Take r 10cm a 2cm R A 200 rad s C 100 rad s R 2 B 0 2 T m 50 gm g 10 m s 100 B 300 rad s D 10 rad s m

A solenoid of radius R and length L has a curren I Io coswt The value of induced electric field a a distance of r outside the solenoid is 1 HonlooR2 2r 3 MonloR2 sin oot 2 HonlooR r gin 4 Zero sin oot

1 Consider an infinite one dimensional wire carrying a uniform current I as shown in the figure A square loop of side a is initially placed such that the center of the loop is at a distance R from the wire where R The square loop is then moved rightwards with a uniform speed u as shown in 2 the figure What is the induced emf in the loop as a function of time t Hola v 2 R vt 2 X 2 X 3 a 11 X 4 3 ola v 2 R vt Hola v 4T R vt 2 a 4 2 a a 3 o Ia v 4T B vt a

A magnetic field B 0 61 is directed upward through a circular loop of diameter 7 cm and 500 turns The loop is initially horizontal so it is perpendicular to the magnetic field It rotates through a horizontal axis so that the plane of the loop is at 74 with the horizontal axis within 1 second What is the magnitude of the induced emf

A semi circular conducting wire of radius 2m is rotated in a uniform magnetic field B 0 1 Tesla 2 about point O with angular speed 10 rad s as shown in the figure The axis of rotation is parallel to B Find magnitude of the potential difference in volt between point M and point N tan 53 3 in and pres 153 M 53 N

The network shown consists of an infinite number of cells of emf and with corresponding internal resistances r and respectively A resistor R 102 is connected to the end of the network If the values of the emfs and internal resistances are 1 0 V 2 2 0 V r 492 and 1 602 If the current flowing through the resistor R is I ampere then find 10 I www ww www f ww E S 1 ww 55 www B wwww

B Normal force exerted by the string on bead is zero C If the wire frame were not present bead execute circular motion and returns to initial point after tracing on a complete circle D Bead would move along a circular path until it reached the opposite starting position and then executes periodic motion The magnetic flux linked with a conducting coil depends on time as 4 6 where n is positive constant The induced emf in the coil is e A If 0 n 1 e 0 and le decreases with time B If n 1 e is constant C If n 1 le increases with time D If n 1 le decreases with time

A circuit shown in figure contains ideal inductor and battery Initially current inductor is zero and the switch is closed at t 0 When potential difference across inductor is 50 of maximum potential difference across it then select correct alternatives R R www Current through battery is R R 7 E 12 R wwww wwwwwwwwww R RR Your Answer

STATEMENT 1 A vertical iron rod has a coil of wire wound over it at the bottom end An alternating current flows in the coil The rod goes through a conducting ring as shown in the figure The ring can float at a certain height above the coil because STATEMENT 2 In the above situation a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the upward direction 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

2 71 A pure inductor coil having inductance L is connected o a resistance R and a cell of emf Vo as shown in the figure Switch S is closed at t 0 a Plot the variation of voltage across the resistance and the inductance as a function of time b Find the time t when the two curves obtained in a intersect c A student decides to start counting time from the instant the current becomes half its maximum value Show the graphical plot of current vs time as obtained by this student R www L ooooo

At a hydroelectric power plant the water pressure head is at a height of 300 m and the water flow available is 100 m s If the turbine generator efficiency is 60 estimate the electric power available from the plant g 9 8 ms 2 A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electrie plant generating power at 440 V The resistance of the two wire line carrying power is 0 5 Q per km The town gets power from the line through a 4000 220 V step down transformer at a sub station in the town a Estimate the line power loss in the form of heat b How much power must the plant supply assuming there is negligible power loss due to leakage c Characterise the step up transformer at the plant Do the same exercise as above with the replacement of the earlier transformer by a 40 000 220 V step down transformer Neglect as hefore leakage losses though this may not be a good assumption voltage transmission involved

Two coils have mutual inductance 0 005 H The current changes in the first coil 100 rad s The according to equation I Io sin wt where Io 10A and w maximum value of emf in the second coil is A 5 57 Your Answer

A superconducting loop of radius R has self inductance L A uniform constant magnetic field B is applied perpendicular to the plane of the loop Initially current in this loop is zero The loop is rotated by 180 The current in the loop after rotation is equal to zero BTR NAST Your Answer

A copper rod of length 2 m is hinged at one of its end and it is rotated with angular speed 2 rad s The plane of rotation of the rod is perpendicular to a uniform magnetic field having magnitude 5 T A bulb of resistance 10 ohm is connected to the rotating rod such that one terminal is at a distance 1 m from the hinge and the other terminal is at the free end The current passing through the bulb will be 4 8 A 1 5 A 3 2 A 2A

A closed coil with a resistance R is placed in a magnetic field The flux linked with the coil is o If the magnetic field is suddenly reversed in direction the charge that flows through the coil will be 1 0 2R 2 O R 3 20 R 4 zero

A conducting ring of radius r is rolling without slipping with a constant angular velocity figure If the magnetic field strength is B and is directed into the page then the emf induced across PQ is Bwr 2 2 2 r Bw 1 Bwr 2 2 3 4Bwr 4 8 X X X X X X X X X X XX X X Xw X X X X X QX X X XPX X X X X

Q 108 A ring of radius r has a uniformly spread charge q on quarter of its circumference The opposite quarter of the ring carries a charge q uniformly spread over it Find the electric potential at a point A shown in the figure Point A is at a distance R r from the centre of the ring r O X X X R A

A coil has 1 000 turns and 500 cm as its area The plane of the coil is placed at right angles to a magnetic induction field of 2 X 10 5 web m The coil is rotated through 180 in 0 2 seconds The average emf induced in the coil in milli volts is

A magnet NS is suspended from a spring and while it oscillates the magnet moves in and out of the coil C The coil is connected to a galvanometer G Then as the magnet oscillates 000 M 1 G shows deflection to the left and right but the amplitude steadily decreases 2 G shows no deflection 3 G shows deflection on one side 4 G shows deflection to the left and right with constant amplitude

12 An L R circuit is powered by a square tooth voltage having a peak value Vo and time period as shown The maximum current in the inductor after a sufficiently large number of cycles is V E A C www R Vo RT 1 07 RT Vo 1 e L R RT J reelle Vo B D 2T 3T t V RT 1 R 1 e RT Vo 1 e L R RT

1 A plane electromagnetic wave propagating in the x direction has wavelength of 6 0 mm The electric field is in the y direction and its maximum magnitude is 33 Vm The equation for the electric field as function of x and t is a 11 sin t x c c 33 sin t x c b 33 sin x 10 t x c d 11 sin x 10 t x c

Which option is incorrect for electrostatic field 1 It is conservative in nature 2 It may be non conservative 3 It follows inverse square law 4 It produces lengthwise contraction betweer dissimilar

96 In capacitor are ideal and source has no internal resistance The circuit is in resonance mooooood Bulb A If a dielectric slab is inserted in the capacitor current will now lag behind the applied voltage B If an iron rod is inserted in the inductor current will now lead the applied voltage C If a dielectric slab is inserted in the capacitor current will now lead the applied voltage D None of these