Magnetic Field Questions and Answers

NCERT EXEMPLAR 1 A square of side L meters lies in the x y plane in a region where the magnetic field is given by B B 21 3 4k T where B is constant The magnitude of flux passing through the square is a 28L Wb b 3BL Wb c 4BL Wb d 29B L Wb

An airplane has an effective wing surface area of 16 m that is generating the lift force In level flight the air speed over the top of the wings is 62 0 m s while the air speed beneath the wings is 54 0 m s What is the weight of the plane Take the density of air 1 29 kg m This is an approximation since the density of air decreases with increasing altitude above sea level

A ball of radius 6 m carries a charge of volume charge density 1 p po 1 2r where po 47 10 c m 4 r is the distance from the centre Find the electric field magnitude at a distance of 8 m from the centre of the sphere

mtG Objective NCERT P The ith 52 ha between the ends of the conductor is act 48 A metal conductor of length 1 m rotates vertical about one of its ends with an angular ve 5 rad s If the horizontal component of ear magnetic field is 0 2 x 10 T then the emf develope a 5 V b 5 mV c 50 V d 50 m 49 A rod of length I rotates with a uniform angle velocity about an axis passing through its midde point but normal to its length in a uniform magne field of induction B with its direction parallel to the axis of rotation The induced emf between the tw ends of the rod is BI a 2 BI h f c 51 A sliding rod AB of resistance R is shown in the figure Here magnetic field B is constant and is out of the paper Parallel wires have 50 A metallic rod of 1 m length is rotated with frequency of 50 revolution per second with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radia I m about an axis passing through the centre and perpendicular to the plane of the ring A constant uniform magnetic field of 1 T parallel to the au is present everywhere The emf between the centre and the metallic ring is a 157 V b 117 V c 127 V d 137 V c v Bd no resistance and the rod is moving with constant velocity v The current in the sliding rod AB when switch S is closed at time t 0 is a R v Bd R t C RIC b zero b d 2BP d OF v Bd R v Bd R URC RC ENERGY CONSIDERATION A QUANTITATIVE STUDY 52 A conducting metal circular wire loop of radius r is placed perpendicular to a magnetic field which varies with time as B Be where B and t are constants at time t 0 If the resistance of the loop is R then the heat generated in the loop after a long Bectromagnetic Induction a c a B c 2TR BR Birw 2R TR 53 In a uniform magnetic field B a wire in the form of a semicircle of radius r rotates about the diameter of the circle with angular frequency to The axis 59 of rotation is perpendicular to the field If the total resistance of the circuit is R the mean power generated per period of rotation is Baru 2R b b a 5 s c 0 05 l s d B 2TR Bir 8R Bitr 8R SL A circular coil of radius 6 cm and 20 turns rotates about its vertical diameter with an angular speed of of magnitude 2 x 10 T If the coil form a closed 40 rad s in a uniform horizontal magnetic field loop of resistance 8 22 then the average power loss due to joule heating is a 2 07 x 10 W c 3 14 x 10 W b 1 23 x 10 W d 1 80 x 10 W 55 A circuit area 0 01 m is kept inside a magnetic field which is normal to its plane The magnetic field changes from 2 tesla to 1 tesla in 1 millisecond If the resistance of the circuit is 2 2 The rate of heat evolved is b 501 s d 0 5J s EDDY CURRENTS 56 A metal plate can be heated by a passing either a direct or alternating current through the plate b placing in a time varying magnetic field 58 c placing in a space varying magnetic field but does not vary with time d both a and b are correct 57 Identify the wrong statement a Eddy currents are produced in a steady magnetic field b Eddy currents can be minimized by using laminated core c Induction furnace uses eddy current to produce heat d Eddy current can be used to produce breaking 60 61

2 A small square loop of wire of side I is placed inside a large square loop of wire of side L The loop are coplanar and their centres coincide What is the mutual inductance of the system a 2 2 Ho 1 TL c 2 2 Ho 12 2 L b 8 2 o 1 RL d 2 2

Electrons mass m charge are accelerated from rest through a potehtal difference V and are then deflected by perpendicular to their velocity The radius of the resulting electron trajectory is ted by a magnet 4

4 10 V 40 The electric and the magnetic field associated with an e m 40 2 3 faya gan fand wave propagating along the z axis can be represented 1 by 1 E E 1 B Boj 05 2 E Ek B B 1 3 E Ej B B 4 E Ej B B k 2 Tom D Tom Cl lom l 23 3 D au fond d Boy 1 E E B B E Ek B B E E B B 1 4 E E B KEai VZE

9 A current of 5 A flows downwards in a long straight vertical conductor and the earth s horizontal flux density is then the neutral point occurs 1 Due north 10 cm from the wire 2 Due east 10m from the wire 3 Due east 5 m from the wire 4 Due west 5 m from the wire

8 A 2 m long solenoid with diameter 2 cm and 2000 turns has a secondary coil of 1000 turns wound closely near its midpoint The mutual inductance between the two coils is a 2 4 x 10 H c 1 28 x 10 H b 3 9x 10 H d 3 14 x 10 H

light disc made of nonmagnetic material is kept horizontally and is free to rotate about its axis as shown in the figure A strong magnet is held vertically at a point above the disc away from its axis On revolving the magnet about the axis of the disc the disc will figure is schematic and not drawn to scale S

magnetic field An e field field the ion on c 40 A rectangular loop of sides 6 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0 4 T directed normal to the loop The voltage developed across the cut if velocity of loop is 2 cm s in a direction normal to the longer side is a 3 8 x 10 V c 2 2 x 10 V b 4 8 x 10 V d 3 2 x 10 V 41 In the question number 40 if velocity is normal in the shorter side then the voltage developed is a 2 3 x 10 V c 4 8 x 10 V 42 The figure shows a wire sliding on b 2 4 x 102V d 1 6 x 10 V xxxxx

The magnetic field of a plane electromagnetic wave is given by B Boi cos kz wt B 3 cos kz wt where Bo 3 10 5T B 2 10 6T The rms value of the force experienced by a stationary charge Q 10 4C at z 0 is closest to

20 A magnetic field B is confined to a region r S 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 Ar The angular velocity to of the ring after the field vanishes is a c 9 Ba 2mb 2mb 9Ba b d 9 Ba 2mb 9 Ba 2mb

omagnetic Induction A coll of mean area 500 cm and having 1000 turns is held perpendicular to a uniform field of 0 4 gauss second The The coil is turned through 180 in average induced emf is a 0 02 V b 0 04 V c 14V d 0 08 V inlenoid with 10 turns per cm has a small incide norm

d q to p in coil A and y to x in coil B 25 The direction of induced current in the right loop in the situation shown by the given figure is Tapping key just closed a along the common axis b along xzy c along xyz d none of these Common axis

17 A loop is formed by two parallel conductors connected by a solenoid with inductance Land a conducting rod of mass m which can freely without friction slide over the conductors The conductors are located in a horizontal plane in a uniform vertical magnetic field with induction B The distance between the conductors is equal to l At the moment t 0 a constant force F starts acting on the rod Angular frequency of motion of rod is oo If F and m are doubled then A w become 1 t times C o become 2 times L www B F constant m l B w become 2 times 1 D w become times 2

c zero d along the magnetic field 34 A conducting loop is placed in a uniform magnetic field with its plane perpendicular to the field An emf is induced in the loop if a it is rotated about its axis b it is rotated about a diameter c it is not moved d it is given translational motion in the field on ir rotated in a magnetic field the 40

92 The surface of a planet is found to be uniformly charged When a particle of mass m and no charge is thrown at an angle from the surface of the planet it has a parabolic trajectory as in projectile motion with horizontal range L A particle of mass m and charge q with the same initial conditions has a range L 2 The range of particle of mass m and charge 2q with the same initial conditions is a L b L 2 d L 4 c L 3

3 A long wire carries a steady current It is bent into a circle Ruch auch B of one turn and the magnetic field at the centre of the Co is B It is then bent into a circular loop of n turns The magnetic field at the centre of the coil will be 3 2nB 1 nB 2 17 B 4 2n B charged particle oves through a uniform magnetic field USA 1 AB 2 n B B B Moo 3 2nB 2R 2 219 B 4 2

mere the earth s 45 57 In the magnetic meridian of a certain place the horizontal component of earth s magnetic field is 0 25 G and dip angle is 60 The magnetic field of the earth at this location is a 0 50 G c 0 54 G b 0 52 G d 0 56 G

58 The equatorial magnetic field of earth is 0 4 G Then its dipole moment on equator is a 1 05 10 A m c 1 05 x 10 A m b d 2 05 x 10 A m 2 05 x 10 Am

a 0 32 G c 4 2 G d 3 2 G 53 Assume the dipole model for earth s magnetic field B which is given by the vertical component of magnetic field By Ho 2mcos8 47 and the horizontal Ho msine 4 component of magnetic field BH where 0 90 latitude as measured from magnetic equator then the loci of point for which dip angle is 45 b tan 2 d tan 1 a tan 3 c tan 0 5 The angler of din at the poles and the equator 60 61 62

a 30 The vertical component of earth s magnetic field at a place is 3 times the horizontal component the value of angle of dip at this place is a 30 b 45 c 60 d 90 in location in Africa compass points 12 58 The its a c 59 A 60

a 30 52 At a certain location in Africa compass points 12 west of geographic north The north tip of magnetic needle of a dip circle placed in the plane of magnetic meridian points 60 above the horizontal The horizontal component of earth s field is measured to be 0 16 G The magnitude of earth s field at the location is a 0 32 G 4 2 G c b 0 42 G d 3 2 G the dipole model for earth s magnetic 59 60

View in English A solid sphere is held at rest on the fixed hemispherical bowl made of insulating material such that centre of sphere lies on the horizontal diameter as shown in figure Total charge q 5 1 x 10 C and mass m 42 grams both are distributed uniformly in the sphere There exists uniform magnetic field B in space as shown in figure Consider contact surface to be sufficient rough Spherical bowl is made of non magnetic material Radius of bowl R 10 cm radius of sphere r 3 cm g 10 m s Now if sphere is released X At an angle 8 with horizontal velocity of COM of sphere will be v 10 7 g R r sin e At an angle 8 with horizontal velocity of COM of sphere will be v g R r sine 8 X Fixed bowl g B The limiting value of B appoximately so that on releasing sphere it do not leaves contact with bowl in course of motion will be 2T The limiting value of B appoximately so that on releasing sphere it do not leaves contact with bowl in course of motion will be 4T

A coaxial cable consists of internal solid conductor of radius a and external thin wall conducting tube of radius b Consider that current distribution over the cross section of the internal conductor is uniform and permeability is equal to unity everywhere Then the inductance of a unit length of cable will be at

3 A circular coil of 100 turns radius 10 cm carries a current of 5 A It is suspended vertically in a uniform horizontal magnetic field of 0 5 T and the field lines make an angle of 60 with the plane of the coil The magnitude of the torque that must be applied on it to prevent it from turning is a 2 93 Nm b 3 43 Nm d 4 93 Nm c 3 93 Nm

35 A uniform horizontal magnetic field of 7 5 x 10 T is set up at an angle of 30 with the axis of an solenoid and the magnetic moment associated with it is 1 28 JT Then the torque on it is a 4 8 x 10 Nm b c 1 2 x 10 Nm 1 6 x 10 d 4 8 x 10 Nm Nm

a 1 2 10 T c 1 2 x 10 T b 2 4 x 10 T d 2 4 x 10 T 37 The magnetic moment of a short bar magnet placed with its magnetic axis at 30 to an external field of 900 G and experiences a torque of 0 02 N m is a 0 35 A m b 0 44 A m c 2 45 A m d 1 5 A m 38 Which of the following is not showing the essential difference between electrostatic shielding by a 42 The a b c d 43 Whic magr a b

39 The net magnetic flux through any closed surface kept in a magnetic field is a zero b d Ho 4x 4 0 TL c 4TH 10 Point out the correct direction of magnetic field in a b d 46 The magn earth a

groun 46 The horizontal and vertical components of earth s magnetic field at a place are 0 3 G and 0 52 G The earth s magnetic field and the angle of dip are a 0 3 G and 8 30 b 0 4 G and 8 40 0 6 G and 8 60 c 0 5 G and 8 50 d

109 0 A short bar magnet placed with its axis at 30 with a uniform external magnetic field of 0 35 T experiences a torque of magnitude equal to 4510 Nm The magnitude of magnetic moment of the given magnet is a 261T c 0 25T b 26JT d 0 026JT

c 38 61 25 A closely wound solenoid of 3000 turns and area of cross section 2 x 10 m carrying a current of 6 A is suspended through its centre allowing it to turn in a horizontal plane The magnetic moment associated with this solenoid is a 12JT 3 01T b 241T d 3 6 JT 32

Two identical magnetic dipoles of magnetic moment 2 A m are placed at a separation of 2 m with their axes perpendicular to each other in air The resultant magnetic field at a midpoint between the dipoles is a 4 5 105 T b 2 5x10 5 T c 4 5x10 7 T d 2 5 107 T

wire is bent to form the double loop shown in figure There is a uniform magnetic field directed into the plane of the loop If the magnitude of this field is decreasing current will flow from X X X X A C X X X a A to B and C to D A to B and D X X X X X B D X X X X X X X b B to A and D to C d B to A and C to D

d 73 A circular coil of radius 10 cm having 100 turns carries a current of 3 2 A The magnetic field at the center of the coil is a 2 01 x 10 T c 2 64 x 10 T b 5 64 x 10 T d 5 64 x 10 T 74 In the question number 73 for the coil given the magnetic moment is a 12 95 A m c 10 05 A m b 25 79 A m d 24 79 A m 75 In the question number 73 the given coil is placed in a vertical plane and is free to rotate about a horizontal axis which coincides with its diameter A uniform magnetic field of 5 T in the horizontal direction exists such that initially the axis of the coil is in direction of the field The coil rotates through an angle of 60 under the influence of magnetic field The magnitude of torque on the coil in the final position is a 25 Nm c 40 Nm b 25 3 Nm d 40 3 Nm

8 A circular coil of 25 turns and radius 12 cm is placed in a uniform magnetic field of 0 5 T normal to the plane of the coil If the current in the coil is 6 A then total torque acting on the coil is a zero b 3 4 Nm c 3 8 Nm d 4 4 Nm

Two shorts magnets of magnetic moments 0 8A m and 2 7A m are placed along the same straight line with their like poles towards each other The distance between their centres is 40 cm The distance of the zero induction point on their common axial line from the centre of the weaker magnet is

79 The final torque on a coil having magnetic moment 25 A m in a 5 T uniform external magnetic field if the coil rotates through an angle of 60 under the influence of the magnetic field is b 108 25 Nm d 258 1 Nm a 216 5 Nm c 102 5 Nm

30 Which of the following statements regarding magnetic lines of force is correct 1 Total magnetic flux linked with a closed surface is always zero 2 They need not be perpendicular to the surface from where they start or where they meet 3 They may or may not pass through a conductor 4 All of these

A long straight conducting solid cylindrical wire of radius R carries a steady current that is uniformly distributed throughout the cross section of the wire Choose the correct graph of magnetic field B versus r where r is distance from the axis of the wire 1 TER BA FRR

4 18 In an electromagnetic pump designed for transferring molten metals in a pipe section with metal is located in a uniform magnetic induction B A current I is made to flow across this pipe section in the direction perpendicular both to the vector B and to the axis of the pipe Find the Gauge pressure produced by the pump if B 0 10T I 100A and a 2 0cm TG4 B Figure 4 254 TI

4 32 Consider the current carrying loop shown in figure 4 258 formed of radial lines and segments of circles whose centres are at point P Find the magnitude and direction of B at point P Ans Ho 11 12 a h Figure 4 258 out of the page a

c 66 5 A m d A m 8 A uniform conducting wire of length length 10a and resistance R is wound up into four turn as a current carrying coil in the shape of equilateral triangle of side a If current I is flowing 60 through the coil then the magnetic moment of the A 60 coil is a c 3a 1 d 24 1 2 a 1 b a 1 3

2 A short bar magnet has a magnetic moment of 0 65 JT then the magnitude and direction of the magnetic field produced by the magnet at a distance 8 cm from the centre of magnet on the axis is a 2 5 x 10 T along NS direction b 2 5 x 10 T along SN direction c 4 5 x 10 T along NS direction d 45x19 T along SN direction

A bar magnet of magnetic moment M is hung by a thin cotton thread in a uniform magnetic field B Work done by the external agent to rotate the bar magnet from stable equilibrium position to 120 with the direction of magnetic field is consider change in angular speed is zero 3MB 2 MB 2

nd B same The A is ying force 12 m ively a 72 2 A m c 74 56 A m b 70 5 A m d 75 56 A m 70 A uniform conducting wire of length 18a and resistance R is wound up as current carrying coil in the shape of a regular a hexagon of sides a If the coil is connected to a voltage source V then the magnetic moment of coil is a 6 3a Am b 7 3 Va Am c d 3 V a 2 R 11 3 Va B D Am Am

7 A 200 turn closely wound circular coil of radius 15 cm carries a current of 4 A The magnetic moment of this coil is a 36 5 A m c 66 5 A m 58 A uniform conducting b 56 5 A m d 108 A m wire of length

QA wire of radius R carries a current I uniformly distributed throughout its interior Which plot best represents the magnitude of the magnetic field as a function of r the distance from the center of the wire

magnet zero Inside core of toroidis 9 The inner and outer radius of a toroid core are 28 cm and 29 cm respectively and around the core 3700 turns of a wire are wounded If the current in the wire is 10 A then the magnetic field inside the core of the toroid is a 2 60 10 2 T c 4 52 10 T b 2 60 10 T d 4 52 10 T