Magnetic Field Questions and Answers

Q 6 Consider two concentric metallic spherical shells of radii a and b Half of the region between them is filled with dielectric of constant k and the other k Inner shell is given charge Q and outer shell Q Determine electric field and potential difference between the shells

In an experiment for positive ray analysis with Thomson method two identical parabola are obtained when applied electric fields are 3000 and 2000 V m The particles are singly ionised particles assuming same magnetic field

Current through an inductor is increasing according to 2t Variation of rate of du increment of its energy d with time tis dt correctly shown in the graph Only One Correct Answer A B dt dit P du

16 When the current flowing in a circular coil i doubled and the number of turns of the coil in is halved the magnetic field at its centre w become sta A 1 Samevom 8 2 Four times 1

A block of mass M placed on another block of mass M is connected to a hanging body of mass m by an inextensible string which passes over a smooth fixed pully If the ground is smooth A The minimum value of m so as to topple the block is 2M 5 B The minimum value of m so as to topple the block is 2M C The minimum coefficient of friction required to topple the block before sliding is m 2M m D The minimum coefficient of friction required to topple the block before sliding is 2m 2M m M M

Consider a non conducting ring of radius a in x y plane The two semi circular portions hav linear charge densities and as shown Then A Dipole moment of the ring is 2 31 B Dipole moment of the ring is 3i C Electric field at the center of the ring is D Electric field at the center of the ring is A 2 E a 3i j 2 2a e a i 33

26 A small bar magnet is placed with its axis at 30 with an external magnetic field of 0 06 T experiences a torque of 0 018 Nm The minimum work required to rotate it from its stable to unstable equilibrium position is A 9 2 10 J B 11 7 x 10 3 J C 6 4 10 2 J D 7 2x 10 2 J

A wire of length 2 m is placed in uniform magnetic field of 2 tesla It makes 30 with the field If 10 A current is flowing in the wire then force per unit length on wire is 1 1 N 3 5 N 2 0 5 N 4 10 N

0 A parabolic section is located in x y plane an cares a current of 12 AA uniform magnet field B 0 4 T making an angle of 60 with x axe exits throughout the plane What is total force on wire between origin and point x 0 25 y 1 00 m 1 1 36K N 2 24 N x y P B

The magnitude of the magnetic field inside a solenoid of length 300 cm and made up of 450 turns is 9 x10 T The current carried by the solenoid is assume the radius of solenoid 300 cm Note For this question discrepancy is found in question answer Full Marks is being awarded to all candidates Options 1 2 3 1 5 A NIE 15 TL A A 25 A

2 A small spherical object having density 2p is placed inside the liquid of density p and connected to an ideal string of length whose other end is kept fixed so that the object can move in a vertical circle minimum speed which must be given at the bottom to just complete the vertical circle Ignore viscosity or any such other drag forces 5gl 2p 2 5gl

sists of nd the er part posite be the ection h the on is 4 25 A charge particle of charge q mass m is projected with a velocity v vi in a region of space where electric field strength E Ek and magnetic induction B Bj are present The acceleration of the particle is A qvB m k q E vB k E 34 AB m 9 Figure 4 223 B qE m k q E vB k

BC in the given Tis ich forms an ernendioulon 4 26 A ring of radius 5m is lying in the x y plane is carrying current of 1A in anti clockwise sense If a uniform magnetic field of magnetic induction B 31 4 is switched on in space then the co ordinates of point about which the loop will have a tendency to lift up is A 3 4 3 3 0 A 5m Figure 4 224 2 4 3 4 0 3 X

4 24 A uniform magnetic field exists in region which forms an equilateral triangle of side a The magnetic field is perpendicular to the plane of the triangle A charge q enters into this magnetic field perpendicularly with speed v along perpendicular bisector of one side and comes out along perpendicular bisector of other side The magnetic induction in the triangle is A mv qa B 2mv qa

4 55 An electron experiences no deflection if subjected to an electric field of 3 2 x 105 V m and a magnetic induction of 2 0 10 T Both the fields are applied perpendicular to the path of electron and also to each other If the electric field is removed then the electron will revolve in an orbit of radius A 45m B 4 5m C 0 45m D 0 045m

7 Two wires carrying currents I and I lie one slightly above the other in horizontal plane as shown in figure The region of vertically upward strong magnetic field is I 0923 810

This is a cyclotron I think the figure is showing wr ong direction of deflection of charge coz using q v xB direction of force is t if the given condition s of downward B and v is satisfied The case that I think should happen is drawn below in the at ached picture X X X X Dees Deflection plate Exit port x ra X X B

A steel bar is heated in a furnace until it reaches 2000 F The blacksmith observes that it cools to 1500 F in 15 minutes It needs to be hammered into shape before it gets within 500 F of the room temperature 100 F before it gets too cold to be shaped properly After pulling out the steel bar from the furnace how long does the blacksmith have before it needs to be reheated Assume that Newton s law of cooling is applicable 76 5 min O 101 8 min 56 6 min 65 6 min

16 Two short bar magnets of magnetic moments M each are arranged at the opposite corners of a square of side d such that their centres coincide with the corners and their axes are parallel to one side of the square If the like poles are in the same direction the magnetic induction at any of the other corners of the square is Mo M 1 AT Ho 2M 2 4n d 3 Ho M 2n d H 2M

A machine gun fires five bullets per second into a target The mass of each bullet is 5gm If the average force required to hold the gun in position is 12 5 N then what is the speed S in m s of each bullet what is the power P in kW delivered to the each bullet Options 1 2 3 4 S 2500 P 6 250 S 2500 P 3 125 S 500 P 3 125 S 500 P 6 250

A uniform rod AB of mass m and length rests on a smooth horizontal surface An impulse Jis applied at a distance rod is B 11 3 O J2ml O4Jlml O 2Jlml O3Jlml View in English 1 3 from centre C of rod as shown Angular velocity of

Assertion The direction of the magnetic field around a current carrying conductor can be determined by using the right hand thumb rule Reason If the first finger points in the direction of the magnetic field and the second finger in the direction of the current then the thumb will point in the divaation EFT a Both A and R are true and R is the correct explanation of A Both A and R are true but R is NOT the correct b explanation of A CA is true R is false d A is false but R is true

21 A magnetising field of 2 x 103 A m produces a magnetic flux density of 8 T in an iron rod The relative permeability of the rod will be 1 102 3 101 ie 2 10 4 104

1 s S figure tan 2 then the correct direction of the magnetic field at P can be shown by the arrow S 1 2 qal beaolo anel 3 1 4 NE 12 0 2 4 4 3 N 5

15 The time period of a freely suspended magnet is T If it is broken along length into two equ parts and one part is suspended in the same way then its time period will be T 2 3 2T 2 T 4 T 2

A case of boundary condition A plate with a z surface normal vector in current density along the x axis in the same direction determine the direction of the magnetic field a Y b y c Z d Z e X

An electron moves with a speed of 3 5x107 m s in the directions shown in Ligure 1 and gure 2 below A060 T magnetic field points in the positive direction Figure 450 2 of 2 Y Y Correct Part C Previous Answers What is the magnitude of the magnetic force in Figura 217 Express your answer with the appropriate units Submit Part D HA Value Repuest Answer 3 zdraction 45 to ty and ta y direction 46 to y and 2 Correct What is the direction of the magnetic force in the Eigure 23 Previous Answers Units

05 A circuit consists of a circular loop of radius R kept in the plane of paper and an infinitely long current carrying wire kept perpendicular to the plane of paper and passing through the centre of loop The mutual inductance of wire and loop will be a HR 2 c R b 0 d HR 2 X R

A wire is bent in the form of a circular arc with a straight portion AB If the current in the wire is i then the magnetic induction at O is A Moi 2 r C Moi 2 r tan tan A B B Moi 2 r D Hoi 2 r tano

Consider a frame made up of uniform wire shown in the figure A time varying magnetic field B bt is switched on Find the charge on the capacitor in steady state L X X X X X X X X X X X X X x X X X X X X X x X 2t

A conducting rod is pushed to the left at a constant speed of v 5 m s along a 10 cm wide conducting rail assume the resistance in the rail is negligible A 1 2 T magnetic field flows out of the page perpendicular to the rail as shown below a The area of the loop in m can be expressed as A t 0 1 1 vt Use Faraday s law to determine the induced voltage in the rod with respect to time Show your work for full credit O 0 6 1 5t O 0 12 1 5t 0 5 O 0 6 O None of the above 10 cm

proton and an alpha particle move in circular orbits in a uniform magnetic field Their speeds are in the ratio of 9 4 The ratio of radii of their circular orbits 3489 Falpha 18 b a 4994

A semicircular loop of mass per unit length 10 kg m is placed on a surface with its plane parallel to the surface in a uniform magnetic field of magnitude 1 Tesla as shown in figure Find the minimum amount of current in A that should be passed in the loop so that it just start to rotate B

Q 34 Given below are two statements labelled as assertion A and reason R Assertion A The current carrying circular copper coil kept inside a uniform magnetic field experiences maximum torque when its plane makes an angle of zero degree with the direction of magnetic field Reason R The torque experienced by the current carrying coil inside a uniform magnetic field is M x B where the symbols have their usual meaning Select the most appropriate answer from the options given below a Assertion and Reason are true and Reason is the correct explanation of Assertion b Assertion and Reason are true but Reason is not the correct explanation of Assertion c Assertion is true but Reason is false d Both Assertion and Reason are false

In the given diagram there are two semicircular parts one having radius a and another having radius 3al as shown If resistance of ACB part is R and resistance of ADB part is 3R Select the correct option s A A Current through ACB is 1 4 C Magnitude of B at O due to ACB part 3 ol 16a is 3a B D B Current through ADB is 1 4 D Magnitude of B at O due to ADB part Hol 48a is

Which of the following statements is true Charges moving in uniform deceleration generate a static magnetic field Charges moving in uniform acceleration generate a static magnetic field Any charge will generate a static magnetic field Charges moving in uniform velocity generate a static magnetic field

Which logic gate is represented by the following combination of logic gates Bo Y Y O NOR OR NAND AND

fig shows certain wire segments joined together to form a coplanar loop The loop is placed on a perpendicular magnetic field in the direction going into the plane of the figure The magnitude of the field increases with time I and I are currents in the segments ab and cd Then X X X X X X X X X X a X X X X X X X x 4 X X X a I 1 b I 1 0 I in the direction ba and I is in the direction cd x x X X X X X X

A wire carrying current has the shape as shown in adjoining figure Linear parts of the wire are very long and parallel to X axis while semicircular portion of radius R is lying in Y Z plane Magnetic field at point O is Z I 02 50 hr min O

A very small current carrying square loop current I of side L is placed in y z plane with centre at origin of the coordinate system shown in figure In List I the coordinate of the points are given in List II magnitude of strength of magnetic field is given Then P0 a Pla a 0 P 0 0 List 1 8 1 P At point 0 0 0 0 fu 0 0 0 0 Q At point P a 0 0 here a L fP a 0 0 a L R At point P 0 a 0 here a L furg P 0 a 0 a L 3 List 11 11 2na 2 24 1 zl H 5113 16xa Codes A 1 1 O 1110

Two discs of radii R and 2R are moving with velocities v and 2v in opposite directions on a conducting platform as shown in the figure If magnetic field B is applied on the plane perpendicular to the discs then the potential difference between two points P and Q which are the topmost points of the discs is Only one correct answer A 8BRv R ARRY 2R 2v

Ques 24 NUMERICAL A copper wire of length 0 5m has a mass 0 05kg If this wire is kept in a magnetic field the minimum current in the wire in order to keep it in equilibrium will be A

4 d 4x Q 174 A rod of length rotates with a uniform angular Q 174 velocity about an axis passing through its middle point but normal to its length in a uniform magnetic field of induction B with its direction parallel to the axis of rotation The induced emf between the two ends of the rods is B 0 1 2 3 B 8 2 zero 4 2B 00 ON 3 STT B Ho 2 2 M 4T 1 G ufa B 2 3 B 8 Ho 2M 4 d o gran a fa que Rafta tega and 2 4 2B 00

D If the uniform magnetic field exist in a regio towards north direction then the direction of forc acting on positively charged particle projected alon east direction is 1 Vertically upward 2 Vertically downward 3 Towards south 4 Towards west

15 A ring of radius R with charge q uniformly distributed over it is rotated with angular speed o around its axis Find magnetic field at the centre of the ring 1 90 2r 2 qw 2 r aw

Aakash Institute 20 The electric field of a plane electromagnetic vaccum is represented by Ex wave in 0 E 0 500s 2x 10 1 1 E 2x10 t direction of propagation of electromagnetic wave 1 ve x axis 2 ve y axis 3 ve z axis 4 ve z axis E 0 What is the

A uniform wire is bent in the form of a circle of radius R A current I enters at A and leaves at C as shown in the figure If the length ABC is half of the length ADC the magnetic field at the centre O will be B O Hol 2R O Hol 4R O Hol 6R O Zero A D Marks 4 1

3 tan 3 4 tan 2 The magnetic field due to a small bar magnet at end on position is making an angle with magnetic moment The value of angle 0 is 1 Zero 2 90 4 tan 2 3 180 her

The magnetic field due a short bar magnet at a distance x from it on the axial line is 0 1 G The magnetic field due to the same bar magnet at a distance 2x on the equatorial line will be 0 1 G 0 2 G 6 25 mG

nstitut owers 0 Datura Musta Gulm 4 Toma n ginger 1 Rhizo 2 Offse 3 Bulbil 20 Ratio of magnetic carrying coil of radius R and at distance of 3R on its axis is 1 10 10 2 20 10 3 2 10 4 10 21 A conduting rod of length I is moving with velocity pendicular magnetic field B Resistance 21