Electromagnetic Induction Questions and Answers

c 1 389 H d 13 89 H a 0 79 W c 2 74 W NEET 2018 An inductor 20 mH a capacitor 100 F and a resistor 50 22 are connected in series across a source of emf V 10 sin 314 t The power loss in the circuit is b 0 43 W d 1 13 W NEET 2018

A vertical ring of radius r and resistance R slips vertically between two frictionless and resistanceless vertical rails The rails which are joined at top There is a uniform magnetic field of magnitude B perpendicular to plane of the ring and the rails When speed of ring is v the current in the section PQ is A zero C 4Brv R B 2Brv R D 8Brv R P

28 A solenoid has 2000 turns wound over a length of 0 3 m The area of its cross section is 1 2 x 10 m Around its central section a coil of 300 turns is wound If an initial current of 2 A is reversed in 0 25 s the e m f induced in the coil is equal to 1 6 10 4 V 2 4 8 10 2 V 3 2 4 x 10 2 V 4 48 kV

Q4 In the circuit shown the switch S has been closed for a long time and them o ens at t 0 12 VT 3 02 wwwwwww 92 S 6Q llllll L 1 H a Find the current through the inductor just before the switch is opened b Find the current through the inductor a long time after the switch is opened c Find current through the inductor as a function of time after the switch is opened Also write the current through the cell as a function of time

228 The following figure shows a conducting rod on two parallel conducting rails The only resistance present in R shown in figure If an unsteady magnetic field B Bot is present in the above region directed along the inward normal to the plane of paper the conducting rod will 1 Move left with a constant speed 2 Move right with a constant speed 3 Move left with a variable speed Move right with a constant variable

carrying current I t kte k 0 as a function of time t20 Counter clockwise current is taken to be positive A circular conducting coil of radius 2R is placed in the equatorial plane of the solenoid and concentric with the solenoid The current induced in the outer coil is correctly depicted as a function of time by JEE Main 2019 9 April Shift II a t 0 c t 0 at b t 0 d t 0

Figure shows a conducting ring A conducting rod of length is hinged at the centre of the ring and its other end touches the ring such that the rod can rotate in the plane of the ring The hinge and the ring are connected by a resistance R There exists a uniform magnetic field given by B Bok in the region x 0 and B Bok if x 0 The rod rotates with constant angular velocity w anti clockwise and the direction of current in the resistance R is shown Taking this direction as positive and the instant shown in figure as t 0 draw a graph showing the variation of current with time B B K 100 4 y axis w C PI R PL www B B K x axis

Figure shows a circular wheel of radius 10 0 cm whose upper half shown dark in the figure is made of iron and the lower half of wood The two junctions are joined by an iron rod A uniform magnetic field B of magnitude 2 00 x 10 exists in the space above the central line as suggested by the figure The wheel is set into pure rolling on the horizontal surface It takes 2 00 seconds for the iron part to come down and the wooden part to go up Find the average emf induced during this period X X X X sosia X XI X X X X iron Figure 38 F9 X X X X wood

69 A semicircular wire is moving with uniform velocity in a uniform magnetic field as shown in figure Hence the wire becomes B X A 1 Electrically charged 2 Positively charged at end B 3 Hot due to Joules heating 4 Both 2 3 X

A highly conducting ring of radius R is perpendicular to and concentric with the axis of a long solenoid as shown The ring has a narrow gap of width 8 in its circumference The cross sectional area of the solenoid is a The solenoid has a uniform internal field of magnitude B t Bo t where 0 Assume that no charge can flow across the gap the face s accumulating an excess of positive charge is are A F B F C F and F both D difficult to conclude as data given are insufficient F Gap of Area a width 8 F

Shown in figure there is a simple network of these resistors R 1 R 20 and Rs 30 A battery of emf 0 3 volt is connected The dimension of the loop are given In loop 1 inward magnetic field B e 2 is applied and in loop 2 outward magnetic field B 2t is applied Find the initial current flown through the resistor R3 and R t is time R A Answer B 20 cm C B e Loop 1 100 cm initial current in Rs 4 initial current in R A 110 initial current in R 110 R R B 2t O Loop 2 100 cm 0 3 V Rate this question

2 The figure shows a rectangular loop with area A 0 2 m and resistance R 222 rotating about the axis given by the dashed line It rotates at a frequency 60 revolutions per second Half of the loop is in a field B 0 1 T coming out of the page and half is in a field B 0 2 T going into the page The figure describes the situation at t 0 The current induced at a time instant t is

space 0 In all other cases Two parallel conducting rails are connected to a source of emf E and internal resistance r Another conducting rod of length l having negligible resistance lies at rest and can slide without friction over the rails A uniform magnetic field B is applied perpendicular to the plane of the rails At t 0 the rod is pulled along the rails by applying a force F The velocity of the rod is observed to be v vo cos wt then find the power in watt spent by the force over 1 cycle Given B 2 Tesla r 2 10 2 vo 2ms l 1cm LT www B xxxxx F e

Two inductors of indu 4H are coupled in series The separation between them and relative orientation is fixed and once they are connected in configuration A and then in configuration B as below ooooooo roooooooooo roooooooooo A ellelle B If the maximum and minimum equivalent inductance of the combination is found to be 16H and 3H the

A thin circular ring of area A is held perpendicular to a uniform magnetic field B A small cut is made in th ring and a galvanometer is connected across the ends such that total resistance of the circuit is R Whe the ring is suddenly squeezed to zero area the charge flowing through the galvanometer is

The magnetic flux in weber in a closed circuit of resistance 100 varies with time in seconds according to equation 6t 5t 1 A the magnitude of induced current at t 0 25s is 0 2A B the change in flux from t 0s to t 1s is 1 weber C the magnitude of induced current t 0 25s is 0 3A D the change in flux from t 0s to t 0 25s is 1 weber

A straight conducting rod of length 30cm and having a resistance of 0 2 ohm is allowed to slide over two parallel thick metallic rails with uniform velocity of 0 2 m s as shown in the figure The rails are situated in a horizontal plane if the horizontal component of earth s magnetic field is 0 3 104 T and a steady current of 3uA is induced through the rod The angle of dip will be 1 tan 2 tan 4 3 tan 3 4 tan 4 A circuit On 3 3 V 0 2m s

6 One conducting U tube can slide inside another as shown in figure maintaining electrical contacts between the tubes The magnetic field B is perpendicular to the plane of the figure If each tube moves towards the other at a constant sped v then the emf induced in the circuit in terms of B 1 and v where 1 is the width of each tube will be x B x A 1 Zero 3 Blv X D X X X X CX 2 2Blv 4 Blv 1 0

The magnetic flux linked with a coil is and the emf induced in it is E then select correct option 1 If 0 E must be zero 2 If 0 E cannot be zero 3 If E is not zero may or may not be zero 4 All of these

Example 21 A uniform wire of resistance per unit length is bent into a semicircle of radius a The wire rotates with angular velocity w in a vertical plane about a horizontal axis passing through C A uniform magnetic field B exists in space in a direction perpendicular to paper inwards X B A 0 O 0 T 2 D a Calculate potential difference between points A and D Which point is at higher potential b If points A and D are connected by a conducting wire of zero resistance find the potential difference between A and C

The variation of magnetic flux with time is shown The variation of induced emf with time is shown as Flux 3 Emf4 M Emf Time Time Time 2 4 Emf Emf Time Time Joon as 2t weber then at what time magnitude of induced

10 The switches in figure 38 Q8a and 38 8b are closed at t 0 and reopened after a long time at t to L R C RC E a E R L Figure 38 Q8 b

6 A circular loop of wire radius R rotates about z axis with angular velocity co The normal to the loop is perpendicular to z axis At t 0 normal is parallel to y axis An external magnetic field B B B k is applied The emf induced in the coil will be a wB sin cot b tr wB sin cot c B cos wat d T B cos cot Z

Two thin semicircular ring of radius R 2 are smoothly joined and is falling with its plane vertical in a horizontal magnetic induction B At the position MNQ the speed of ring is V The potential difference developed across the points M and Q is A zero B BV R2 2 and M is at higher potential C RBV and Q is at higher potential D 2RBV and Q is at higher potential R 2 R 2

For the coil in the diagram below when the switch is pressed a what is the polarity of end A b which way will the compass point then A B mio 1 AN

22 The inductance of a closed packed coil of 400 turns is 8 mH A current of 5 mA is passed through it The magnetic flux per turn is H Permeability of free space 1 3 1 Ho Wb 4t 1 Ho Wb 1 2 12 17 14 2 Ho Wb 4 0 4 Wb

A thin circular ring of radius R is falling with its plane vertical in a horizontal magnetic induction B At the position MNQ the speed of ring is vo What is the potential difference developed across the ring XX XX X X X X x xBx x X X X X X XX X X X X X XXX Nx X X X X X XX M X X Voy X X X

11 A wooden stick of length 3 is rotated about an end with constant angular velocity to in a uniform magnetic field B perpendicular to the plane of motion If the upper one third of its length is coated with copper the potential difference across the whole length of the stick is Tricky 9Bol X X X a X X X X X X b 2 4Bwl 2 5Bol X X 2 Bol X X X X x x3l X X XX X X X X X X X X X X X w copper XX coat X X X X XX XX XX XX c d 2 X X X X X X X X 12 A uniform magnetic field of induction B is confined to a X X X

2 A thin uniform conducting rod MN of length m starts sliding from 3 rest from initial vertical position between two smooth perpendicular non conducting surfaces as shown A uniform magnetic field B 3 Tesla is existing perpendicular to the plane of motion of the rod When the rod makes an angle 0 37 with the vertical surface then choose the correct option s g 10 m s M A The angular velocity of the rod about its centre of mass is 3 rad s B The motional emf induced between the ends M and N of the rod is 0 56 volt C The motional emf induced between the mid point C and the end N of the rod is 0 78 volt D The motional emf induced between the mid point C and the end N of the rod is 0 39 volt of light of wavelength 5000A and m 1 2 N

Two circular similar coaxial loops carry equal currents in the same sence If the loops are brought nearer what will happen 1 Current will increase in each loop 2 Current will decrease in each loop 3 Current will remain same in each loop 4 Current will increase in one and decrease in the other

Consider a region of cylindrical magnetic held changing with time at the rate x A triangular conducting loop PQR is placed in the field such that mid point of side PQ coincides with axis of the magnetic field region PQ 2l PR 2l E m f induced in the sides PQ QR PR of the loop are Critical Thinking a xl 0 xl b 0 xl 3xl 2 2 c 0 xl xl d 0 x 2 xl2 2 X X X X X X X P X X X 7R X XQX X X X X X X X X

A uniformly wound solenoidal coil of self inductance 1 8 x 104 Henry and resistance 62 is cut into two identical coils They are now connected in parallel across a 12 volt battery of negligible resistance Find the current drawn by the circuit in amp neglecting the mutual inductance between the cut parts of the solenoid

value of electric field in a region where electromagnetic wave is propogating is E then instantaneous value of energy density in the space is E is peak value of electric field 1 1 E 3 E 1 2 E 4 E

A conducting bar of length D rotates with angular frequency w about a pivot P at one end of the bar see the figure The other end of the bar is in slipping contact with a stationary conducting wire in the shape of a circle we only show a small part of that circle to keep the drawing simple Between point P and the circular wire there is a resistor R as shown Thus the bar the resistor and the arc form a closed conducting loop The resistance of the bar and the circular wire are negligibly small There is a uniform magnetic field B everywhere it is perpendicular to the plane of the paper as indicated What is the induced current in the loop Express your answer in terms of D w R and B BO D W

3 3 A conducting circular loop of face area 2 5 x 10 m is placed perpendicular to a magnetic field which varies as B 0 20 T sin 50r st a Find the charge flowing through any cross section during the time t 0 to t 40 ms b If the resistance of the loop is 10 find the thermal energy developed in the loop in this period

3 A coil having n turns and resistance Ris connected in series to a galvanometer of resistance 4R Q This combination is moved in time t second from a magnetic flux W weber to W weber The induced current in the circuit is 1 3 W W 5Rnt W W Rnt 2 4 n W W 5Rt n W W Rt

d is initially attracted and If the instantaneous magnetic flux and induced emf produced in a coil is o and E respectively then according to Faraday s law of electromagnetic induction a E must be zero if o 0 c E0 but o may or may not be zero b E0 ifo 0 d E 0 then o must be zero

A 25 cm long solenoid has radius 2 cm and 500 total number of turns It carries a current of 15 A If it is equivalent to a magnet of the same size and magnetization M magnetic moment volume then M is 1 2 3 4 3T Am 1 30000 Am 1 300 Am 1 30000T Am

Four identical conducting rods are connected by pins The velocity of point R is v A uniform magnetic field B acts out of the paper Choose the correct statement s PQ PS 4l and QR SR 3 6Blv 5 3Blv 5 3Blv A The motional emf across PQ is B The motional emf across PQ is C The motional emf across QR is D The motional emf across QR is 6Blv 5 37 3l C

50 The Network shown in Figure is a part of the circuit The battery has negligible resistance A R 222 E 12V L 5mH oo I B At a certain instant the current I 2A and it is decreasing at the rate of 102 As What is the potential difference between the point B and A GUJCET 20151

At the geomagnetic pole a compass needle 1 Stay in North South direction 2 Stay in East West direction 3 Move in vertical plane 4 Stay in any position

In figure there are two sliders and they can slide on two frictionless parallel wires in uniform magnetic field B which is present everywhere The mass of each slider is m resistance R and initially these are at rest Now if one slider is given a velocity Vo the velocity of other slider after considerably long time will be neglect the self induction A C Vo Vo B 2 D Zero X

9 A conducting rod PQ is rotated in a magnetic field B about an axis passing through point O as shown in figure Then potential difference between P and Q is angular speed Q 1 B b a2 3 BO Boa P og 2 4 b Bob 2 Bo a

A long solenoid has self inductance L If its length is doubled keeping total number of turns constant then its new self inductance will be L 1 2 2 2L 3 L 4 L

conducting loop is placed in a magnetic uniform as shown in figure For this situation mark the correct statement 3 B A The force of compression experienced by loop is IRB B The force of compression experienced by loop is 21RB C The force of expansion experienced by loop is IRB 01029

3 The number of turns in the coil of an ac generator is 5000 and the area of the coil is 0 25 m The coil is rotated at the rate of 100 cycles s in a magnetic field of 0 2 W m 2 The peak value of emf generated is nearly 1 786 kV 3 220 kV 2 440 kV 4 157 kV

5 A bar magnet is released from rest along the axis of a very long vertical copper tube After some time the magnet a will stop in the tube b will move with almost contant speed c will move with an acceleration g d will oscillate 1

uced current for the with respect to time ob O ii I v observer Clas O 821 CHID vi W O O

loop 6 Figure 38 E5 shows a square loop of side 5 cm being moved towards right at a constant speed of 1 cm s The front edge enters the 20 cm wide magnetic field at t 0 Find the emf induced in the loop at a t 2 s b t 10 s c t 22 s and d t 30 s n B 0 6 T X X X X X X X X X X X X 120 cm 38 E5 X X X X X une X X X

1 The coefficient of self induction of two inductor coils are 20 mH and 40 mH respectively If the coils are connected in series so as to support each other and the resultant inductance is 80 mH then the value of mutual inductance between the coils will be 1 5 mH 2 10 mH 3 20 mH 4 40 mH