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Q.2. A solenoid has an inductance of 10 H and a resistance of 2 . It is connected to a 10 V battery.

How long will it take for the magnetic energy to reach4

1 of its maximum value?

Q.3. A conducting ring of radius r is rolling withoutslipping with a constant angular velocity . If themagnetic field strength is B and is directed into thepage then find emf induced across PQ.

P

Q

Q.4. There is a circular region of radius R in which

magnetic field is varying asdt

dB. A horizontal rod

AB of length L is placed as shown in figure. Point Cis centre of the circle and also the mid point of rod.Find the potential difference between A and B.

C

R

x x x x x x x x x x x

x x x x x x x x

A B

Q.5. A conducting loop has an area A = 800 cm2 and incorporatesa capacitor with capacitance C = 10.0 F. It is placed in auniform magnetic field perpendicular to the magneticinduction lines, the magnetic induction varying as B = (8 + 5t) 10 ––2T.Determine :(a) The maximum charge on the capacitor(b) The maximum energy stored in the capacitor(c) Which plate (A or B) will be charged positively.

x x xx

x

x

x x

x

xxxx

x

x

x

x

x

x

x

x

B A C

x x

xx

Q.6. The network shown in the adjacent figure is a part of a

Q.1. As shown in the figure, a metal rod makes contact with apartial circuit and completes the circuit. The circuit area isperpendicular to a magnetic field with B = 0.25T. If theresistance of the total circuit is 3, what force is neededto move the rod with a constant speed of 4 m/s asindicated in the figure ?

50 cm v = 4m/s

B = 0.25 T(into page)

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complete circuit. What is the potential difference VB V A,when the current I is 5A and is decreasing at a rate of103 A/s?

1 15V 5mH

I A B

Q.7. Find the current provided by the sourceimmediately after the switch is closed at t = 0 and

also at t = infinity.

R2 = 10 L= 1 mH

R1 = 10

E = 10 VSw

Q.8. Find the average current in terms of I0,in the graph as shown in the figure

I0

T T 3T

4 2 4

current

time

T

Q.9. A metallic rod of length & resistance R is free to rotate about oneof its ends over a horizontal smooth, rigid circular metallic frame ofradius in an inward magnetic field of induction B. The circuit iscompleted by means of a conducting wire connected between thecentre O and the point on the ring. What torque should be appliedby an external agent to rotate the rod with constant angularvelocity? What is the power expenditure of the external agent?

B

O

wire

Q.10. In the circuit shown, current at the given instant is 1amp, and it is decreasing at a constant rate of 10 3

amp/sec., Find V A-VB between the terminals A and B.

AB

R=10

L=10 mHE=4v

Q.11. A solenoid of inductance 100 mH and resistance 20 is connected to a cell of emf 10 V att = 0. Find the energy stored in the inductor when the time t = 5 ln2 milliseconds.

Q.12. A metallic cylindrical rod PQ slides withoutfriction on a rectangular circuit composed ofperfectly conducting wires fixed on inclinedplane as shown in the figure. A vertical

magnetic field B

exists in the region of theabove mentioned setup. Find the velocity of

the rod PQ when it starts moving without anyacceleration ?

vP

Q

L

B

Q.13. (b) A semicircular wire frame ABC is moved alongit's plane in magnetic field with velocity V asshown in figure, find emf developed a cross AC.

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

A

C

VB

R


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Q.14. A rectangular flat loop of wire with dimensions and b has N turns and a total resistance R. Theloop moves with constant velocity v from positionPQRS to PQRS through a region of constantmagnetic field B as shown in figure(a) Plot the graph of the flux linked with loop vs x.

(Where x is the distance moved by the loop)

× × × × × × ×

× × × × × × ×

× × × × × × ×

× × × × × × ×b b2b

Q Q

x = 0 x = 2b

P

S R

P

S R

(b) Plot the graph of the emf induced in the loop vs x.

Q.15. A conducting rod makes contact with a partialcircuit and completes the circuit as shown. Thecircuit area is perpendicular to a magnetic fieldwith B = 0.25 T. If the resistance of the total circuitis 5 , how large force is needed to move the rodas indicated with a constant speed of 4 m/s apart

from the force F = 1/ 80 N already acting on it in

the direction shown ?

50 cm v = 4m/s

B = 0.25 T

F

Q.16. A solenoid of inductance 100 mH and resistance 20 is connected to a cell of emf 10 V att = 0. Find the energy stored in the inductor when the time t = 5 ln2 ms.

Q.17. A wheel with six spokes is positioned perpendicularto a uniform magnetic field B of magnitude 0.5 T.The field is directed into the plane of the paper andis present over the entire region of the wheel asshown in the figure. When the switch S is closed,there is an initial current of 6A between the axleand the rim; and the wheel begins to rotate. Theresistance of the spokes and of the rim isnegligible.(a) What is the direction of rotation of the wheel?(b) The radius of the wheel is 0.2 m . Calculate theinitial torque on the wheel .

S

Q.18. A constant potential difference of 60 V is suddenlyapplied to a coil which has a resistance of and a selfinductance of 8mH. At what rate does the current beginto30 rise? What is the current at the instant the rate ofcharge of current is 500 A/s ? What is the final current ?

30

60 V

8 mH

Q.19. As shown in the figure, a metal rod makes contactwith a partial circuit and completes the circuit. Thecircuit area is perpendicular to a magnetic fieldwith B = , how large force is0.15T. If theresistance of the total circuit is 3 needed to movethe rod as indicated with a constant speed of 2m/s ?

50 cm v = 2m/s

B = 0.15 T(into page)

Q.20. A very small circular loop of radius a is initially coplanar and concentric with a much larger circularloop of radius b (a < < b). A constant current i is passed in large loop, which is kept fixed in space,and the small loop is rotated with angular velocity about a diameter. The resistance of the smallloop is ‘R’. If its self inductance is negligible. Find(a) current in small loop as a function of time.


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(b) induced emf in large loop as a function of time.

Q.21. A conducting rod 'OA' of mass 'm' and length 'l' iskept rotating in a vertical plane about a fixedhorizontal axis passing through 'O'. The free end 'A'is arranged to slide on a fixed conducting ring

without any friction. A uniform and constantmagnetic field 'B' perpendicular to the plane ofrotation is applied. The point 'O' and the point 'C'(on the ring) are connected by a series combinationof 'R' a resistor 'R' and an inductor 'L' through aswitch 'S'. The angular frequency of the rod is .Initially the switch is opened. Neglect any otherresistance.

A

XB

Y

O

S

R

L

x

x

x

xx x x

x x

xx

x x

xx

x

x xxxxx

x x

C

(a) Find the e.m.f. induced across the length of the rod.(b) The switch is closed at time t = 0 .(i) Obtain an expression for the current in the resistor as a function of time(ii) In the steady state find the torque needed to maintain the constant angular speed of the

rod. The rod was initially along the positive X-axis.

Q.22. The arrangement shown is placed in a uniform verticalfield of strength 3 tesla. Initially both the rods are atrest. The system is released at t = 0. Find thevelocity of the rod of mass m as a function of time.Neglect friction. Takem = 1 kg.

R = 54

B= 3 Tesla

2mm = 1m.

3m

Q.23. In the co-ordinate system shown in thefigure magnetic field is directed alongnegative z-axis and its magnitude varies

as B =x

B0 , where B0 is a positive

constant. A square loop ABCD of side ‘a’and resistance per unit length ‘’ is movedwith constant speed v with its planeparallel to x-y plane. Initially side AB wason the y-axis. Find the current induced inthe loop as a function of time.

BY

A

C

D

X

Z

Q.24. A long conductor is placed inhorizontal plane carrying current (3 +4t2). Assume loop having side 0.25 mis placed in same plane at a distance1m from conductor as shown in figure.Loop is connected by an inductor,having inductance 5 H.Find current in inductor as function oftime assume t = 0, current startsflowing in conductor.

0.25 m

0.25 m

L =5H

1 m

I =(3+4t2)


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Q.25. A conducting square loop of side a2 is rotatedin a uniform magnetic field B about P in theplane of the paper as shown in the figure.(a) Find the induced emf between P and Q and

indicate the polarity of the points P and Q.(b) If a resistance R is connected between Pand Q, determine the current through theresistor.

P

B

Q

Q.26. A ring of radius R made up of a conductingwire whose cross section a is placed in amagnetic field perpendicular to the plane.The magnetic field varies with time asB = B0 sin 2ft. where B0 is a constant.

R

xx

x

x

xxx

x

x

x

x

x

x

xxxxx

x

x

x

x x x x

x

xx

x

xx

x

(a) find the induced emf in the ring.(b) find the resistance of the ring if the resistivity of the material is .(c) What is instantaneous power loss due to current in the ring?

(Ignore the self induced currents in the ring.)

Q.27. Two long parallel horizontal rails, a distance 20 cm apart, eachhaving a resistance 0.2 /m per unit length, are joined at oneend by a resistance 500 . A perfectly conducting rod MN ofmass 0.2 kg is free to slide along the rails without friction.There is a uniform magnetic field of induction 50T normal to theplane of the paper and directed into it. A variable force F is

applied such that a constant current, 2 Amp, flows through R.

R

F d

M

Nx

Bx x xx x x

x x x

x x xFM

(a) Find the magnetic force FM on the rod, and the induced emf as a function of the distance, 10

cm.(b) Find the velocity of the rod, and the applied force F as a function of the distance 10 cm of therod from R.(c) What fraction of the work done by F is converted into heat?

Q.28. In the figure shown, Resistance per unitlength of a square loop of side ‘a’ is .Find the current in the loop as a functionof time if x varies as x = vt, where v is aconstant.

x

vI

Q.29. An inductor of inductance 2.0 mH is connected across a charged capacitor of capacitance 5.F,and resulting LC circuit is set oscillating at its natural frequency. Let Q denote the instantaneouscharge on the capacitor, and I the current in the circuit. C.It is found that the maximum value of Qis 200

(a) When Q = 100C, what is the value ofdt

dI

(b) When Q = 200C, what is the value of I ?(c) Find the maximum value of I.


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(d) When I is equal to one half its maximum value, what is the value of |Q| ?

Q.30. (a) A closed circuit in steady state consists of a battery of 20 volt and a coil of inductance 0.2 H andtotal resistance of the circuit equals 2 . At the moment t = 0 the inductance of the coil is suddenlydecreased to 1/10 times. Find the time dependent expression for the current.

(b) A square loop of side 1m and a long straightconductor carrying a current of 5A are located in thesame plane. Resistance of the loop is 1 . The loop isturned through an angle of 1800 about an axis PQ. AxisPQ is at a distance of 3m from the current carryingconductor. Find the electric charge having flown throughthe loop.

5A

3m1m

P

Q

Q.31. A constant potential difference of 60 V is suddenly appliedto a coil which has and a self inductance of 8mH. At whatrate does the resistance of 30 current begin to rise? Whatis the current at the instant the rate of change of current is500 A/s? What is the final current ?

30

60 V

8 mH

Q.32. An inductor of inducance 2.0 mH is connected across a charged capacitor of capacitance5.0F and the resulting LC circuit is set oscillating at its natural frequency. Let Qdenotes the instantaneous charge on the capacitor and I the current. It is found that themaximum value of Q is 200 C.(a) When Q = 100 C, what is the value of | dI/dt |?(b) When Q = 200 C what is the value of I

(c) When I is equal to one-half its maximum value, what is the value of | Q |

Q.33. In the above figure, PQ is an infinite wire carryingcurrent I as shown. MN is a rigid conducting rod thatcan slide smoothly on parallel rails XX and YY. MNwas coincident with resistance R at t = 0. Find theforce required to pull rod MN away from PQ with aconstant velocity ‘v0’ as a function of time.

X

Y

M

N

d

X

Y

I

Q

P a

Q.34. An L-C circuit consist of an inductor with L = 0.09 H and a capacitor of C = 4.00 10-4 F. The initial

charge on the capacitor is 5.00 C and the initial current in the inductor is zero. (a) Find the valueof maximum current in the inductor.(b) When the current in the inductor has half its maximum value, what is the charge on thecapacitor.


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Q.35. A charge particle of charge q and mass m is projected withvelocity v

in x-y plane making an angle with the x-axis, from the

origin of coordinates. A uniform magnetic field B

also acts alongthe x-axis. Find the position coordinates of the particle at a time

mt

2qB

.

X

B

Y

m

q

v

Z

Q.36. Two conducting rails separated by a distance are joinedat the top by a resistance R. The rails are inclined at anangle with horizontal. A conducting wire MN of mass mand length . Slides without friction on rails with constantspeed v. The conducting wire and rails have no resistance.

A uniform magnetic field B

acts horizontally andperpendicular to the wire MN. Find value of the magneticfield B.

B

R

M

v

N

Q.37. (a) The current in a certain circuit varieswith time as shown in figure. Find theaverage current and the rms currentin terms of I0.

i0

-i0

t 2

(b) A voltage source v = 10 sin 2t volt isconnected to the circuit as shown in thefigure. Find the energy dissipated

through the resistor in first 0.5 sec ?

~

V = 10 sin 2t

1 k

Q.38. Calculate the(i) impedance (ii) current (iii) phase(iv) power factor for the circuit shown inthe figure ~

220 V, 60 Hz

8 XL = 14 XC = 20

Q.39. A thermocole vessel contains 0.5 kg of distilled water at 300 C. A metal coil of area5 10-3 m2, number of turns 100, mass 0.06 kg and resistance 1.6 is lying horizontally at thebottom of the vessel. A uniform, time varying magnetic field is set up to pass vertically through the

coil at the time t = 0. The field is first increased from zero to 0.8 T at a constant rate between 0 and0.2. s and then decreased to zero at the same rate between 0.2 and 0.4 s. This cycle is repeated12000 times. Make sketches of the current through the coil and the power dissipated in the coil asfunctions of time for the first two cycles. Clearly indicate the magnitudes of the quantities on theaxes. Assume that no heat is lost to the vessel or the surroundings. Determine the finaltemperature of the water under thermal equilibrium. Specific heat of the metal = 500 Jkg-1K-1 andthe specific heat of water = 4200 Jkg-1K-1. Neglect the inductance of the coil.


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Q.40. An equilateral triangular conducting loop of side a andresistance R is placed adjacent to a current carrying longstraight wire in same plane, such that distance between wireand side of loop is d. Current is given as I = I0 sin t, then findthe current in the loop as function of time.

a

d

I = I0 sin t

Q.41. A coil of inductance L connects the upper ends of two vertical copper bars separated by a distance . A horizontal conducting connector of mass m starts falling with zero initial velocity along the barswithout loosing contact with them. The whole system is located in a uniform magnetic field Bperpendicular to the plane of the bars. Find the law of motion x (t) of the connector.

Q.42. A loop is formed by two parallel conductors connected bya solenoid with inductance L and a conducting rod ofmass m which can freely (without friction) slide over theconductors. The conductors are located in a horizontal

plane in uniform vertical magnetic field B. The distancebetween the conductors is . At the moment t = 0, the rodis imparted an initial velocity v0 directed to the right.(a) Show that rod will oscillate simple harmonically.(b) Find angular frequency of simple harmonic motion.

mv0

x

Q.43. Two parallel vertical metallic rails AB and CD areseparated by 1m. They are connected at the two endsby resistances R1 and R2 as shown. A horizontalmetallic bar L of mass 0.2 kg slides without friction,vertically down the rails under the action of gravity.There is a uniform horizontal magnetic field of 0.6 Tperpendiculars to the plane of rails. It is observed thatwhen the terminal velocity is attained. The powersdissipated in R1 and R2 are 0.76 W and 1.2 Wrespectively. Find the terminal velocity of the bar Land the value of R1 and R2.

R1

R2

L

A C

B D

Q.44. Find the frequency of the LC circuit shown in figure(a)

C

L

L

L


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(b) A circuit containing a two position switchS is shown in figure.(i) The switch S is in position 1. Find thepotential difference V A - VB and the rate ofproduction of joule heat in R1.(ii) If now the the switch S is put in position

2 at t = 0, find the time when the current inR4 is half the steady value. Also calculatethe energy stored in the inductor L at thattime.

R4

10 mH

23V

R2 B

R512F2

R3

R1

2 12V

E1

E21

2

C

A

3

S

Q.45. A metal rod OA of mass m and length r is keptrotating with a constant angular speed in avertical plane about a horizontal axis at the endO. The free end A is arranged to slide withoutfriction along a fixed conducting circular ring inthe same plane as that of rotation. A uniform

and constant magnetic induction B is appliedperpendicular and into the plane of rotation asshown in figure.

C

L

R

S

OX

A

An inductor L and an external resistance R are connected through a switch S between the point Oand a point C on the ring to from an electrical circuit. Neglect the resistance of the ring and the rod.Initially, the switch is open.(a) What is the induced emf across the terminals of the switch?(b) The switch S is closed at time t = 0

(i) Obtain an expression for the current as a function of time.(ii) In the steady state, obtain the time dependence of the torque, rod OA was along the positive X– axis at t = 0.

Q.46. XY is an infinite current carrying wire carrying a current I. AB is aconducting rod of length L rotating about its centre O with anangular velocity ‘’. At the instant shown it is perpendicular tothe wire XY and end B is at a distance ‘d’ from wire XY.Calculate the emf induced between centre O and point B at thisinstant (vB – v0 = ?)

O

B

A

L

d

X YI

Q.47. In the adjoining diagram, a current-carrying loop pqrs is placed withits sides parallel to a long current-carrying wire. The currents i1 andi2 in the wire and loop are 20 A and 16 A respectively.If a = 15 cm, b = 6 cm and d = 4 cm, what will be the force oncurrent-loop pqrs? What will be the difference in the force, if thecurrent i2 in the loop is clockwise instead of anticlockwise?

a

qp

s

i2

i1

br

d

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