Magnetic Field Questions and Answers

4 23 In the figure 4 222 the force on the wire ABC in the given uniform magnetic field of magnetic induction 2T is A 4 3 2 N C 30 N A X X I 2A X 3m X X Figure 4 222 Bal B 20 N D 40 N 4m

A 4 16 Two long conductors are arranged as shown above to form overlapping cylinders each of radius r whose centers are separated by a distance d Current of density J flows into the plane of the page along the shaded part of one conductor and an equal current flows out of the plane of the page along the shaded portion of the other as shown in figure 4 218 What are the magnitude and direction of the magnetic induction at point A B C D Ho 2 d Ho 2 r dJ in the y direction Kd Mo 4d j 2 r Mo Jr 2 d X Vaccum Figure 4 218 in the y direction in the y direction in the y direction Conductor YA

A solenoid has 450 loops each of radius 0 0254 m The field increases from 0 T to 3 00 T in 1 55 s What is the EMF generated in the coil Hint What is the area of a circle Unit Volts Prezu EME V

5 31 A galvanometer is connected to the secondary coil The galvanometer shows an instantaneous maximum deflection of 7 divisions when current is started in the primary coil of the solenoid Now if the primary coi is rotated through 180 then the new instantaneous maximum deflection will be B 14 units D 21 units A 7 units C 0 units

Q15 Assertion Magnetic fields produced by current carrying circular coil are in form of straight lines at the centre Reason Magnetic field is non uniform and parallel to the plane of the coil 1

85 The effective magnetic moment of the system shown in the figure below is p is the pole strength and 2a is the length of each side of the triangle 1 2ap 3 3ap 2a 2p 60 p 60 2a 2a P 2 ap 4 2 3ap

An equilateral triangle is formed by three wires each of length a carrying a current i as shown in figure The magnetic field at P which lies on a line perpendicular to the plane of the triangle passing through the centre of triangle at a distance a 2 from the centre will be

A square coil ACDE with its plane vertical is released from rest in a horizontal uniform magnetic field B of length 2L The acceleration of the coil is 2L x X O LLJ B X A less than g for all the time till the loop crosses the magnetic field completely B less than g when it enters the field and greater than g when it comes out of the Field C g all the time D less than g when it enters and comes out of the field but equal to when it is within the field

4 49 An electron is projected with velocity vo in a uniform electric field E perpendicular to the field Again it is projected with velocity vo perpendicular to a uniform magnetic field B If r is initial radius of curvature just after entering in the electric field and r is initial radius of curvature just after entering in magnetic field then the ratio r r is equal to

4 53 Infinite number of straight wires each carrying current I are equally spaced as shown in the figure 4 232 Adjacent wires have current in opposite direction Net magnetic induction at point Pis 30 30 2 3 4 Figure 4 232 5 ZA YA X

4 58 The magnetic induction normal to the plane of circular coil of n turns and radius r which carries a current i is measured on the axis at a small distance h from the centre of the coil This is smaller than the mangetic induction at the centre by the fraction A C 2h 37 2 r 3 h 2p B D 3 2 2 h 2 h 2 3

Direction Question is based on the following paragraph A wire of length L mass m and carrying a current is suspended from point O as shown An infinitely long wire carrying the same current I is at a distance L below the lower end of the wire Given I 2A L 1m and m 0 1 kg In 2 0 693 Q What is angular acceleration of the wire just after it is released from the position shown

4 57 A mass spectrometer is a device which select particle of equal mass An ion with an electric charge q 0 starts at rest from a source Sand is accelerated through a potential difference V It passes through a hole into a region of constant magnetic field B perpendicular to the plane of the paper as shown in the figure 4 233 The particle is deflected by the magnetic field and emerges through the bottom hole at a distance d from the hole The mass of the particle is top A C qBd y qB d 8V Figure 4 233 B D qB d 4V qBd 2V

Figure 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 2s b t 10 s and c t 22s B 0 6 T X X X a 3 x 10 V b Zero c 3 10 4 a 3 10 V b 3 10 a Zero b 3 10 V a 3 10 V b Zero V c Zero c 3 10 4 V c 5 x 104 5cm X X X X X X X X X X X X X X X X X 20 cm Marks 4 1

Five parallel infinite wires are placed at the vertices of a regular pentagon Four wires carry current lo each while the fifth wire carries current 3l as shown The resultant magnetic field at the centre O is A zero B Holo C Holo 2 D infinite lo To a a a 310

This is the derivation for time period of ring Module page 69 But in page 72 the ans written is different This is page 69 If a x E F The force on a negative point charge q is 29 280a Q 2 a 2 X 3 4 4 2a x kx where k X x where is the linear charge density m T 2T 2 a k It should be noted that if x is not negligible relatash Educational vices Limited about the centre but the motion will not be simple harmonic On releasing the point charge q of mass m it will E 29 28 m 29 as lava IT JE Foundation This is page 72 Please explain the derivation and what is the difference between th both formulas Electric field on the axis of a uniformly charged ring of dius Qx 4 R x to a the negative charged particle will oscillate 3 where Q is total charge on the 1 if x a with the time period E callittu a distance x from the centre is R at x 1 Time period of SHM 2 of Aakasher 4TE MR

A uniform magnetic field is confined within a cylindrical region as shown If r particles with different speeds enter the region radially then B A Faster the particle lesser is the time spent in region B Slower the particle lesser is the time spent in region C Slower the particle greater is the time spent in region D Time will be same for all particles

In given diagram there is a conducting sphere of radius r which is surrounded by dielectric layer with relative permittivity e If conducting sphere is given charge q then surface density of polarization charges on outer surface of dielectric layer is A q 4f r2 B 9 4f C 1 q Afr D 1 q 4f

through a region of uniform magnetic field No deflection from this straight path is observed Melectron 9 1 x 10 31 kg Gelectron 1 6 10 16 C Instructions In a neat and organized fashion write out a solution which includes the following 1 A sketch of the physical situation with all given physical quantities clearly labeled If the description above consists of an initial and final state both of

3 3 x 10 2 N m 4 3 x 10 3 N m A particle having a mass of 0 01 kg carries a charge of 3 C The particle is given an initial horizontal velocity of 2 x 105 ms in the presence of electric 1 field E and magnetic field B To keep the particle moving in a horizontal direction which is correct 1 B should be perpendicular to the direction of velocity and E should be along the direction of velocity 2 Both B and E should be along the direction of velocity 3 Both B and E are perpendicular to the direction of velocity 4 B should be along the direction of velocity and E should be perpendicular to the direction CROP ENG 17 18 MAGNETIC EFFECT EMI P65

5 A magnetising field of 1200Am 1 produces a net magnetic flux 2 4x10 7 weber in a paramagnetic bar of cross sectional area 0 2 cm The susceptibility of the bar will be 1 17 75 3 24 2 25 4 26 trenvon

0 4 30 In a gravity free space a smooth insulating ring of radius R with a bead having charge q is placed horizontally in a uniform magnetic field of induction Bo and perpendicular to the plane of ring Starting from t 0 the magnetic field is varying with time as B t B at where a is a positive constant The contact force between the ring and bead as a function of time is 0 A C aq Rt m aq Rt 4m 2B at Bo at B D aq Rt 4m 2B out 4aq Rt m 2B at

4 15 A current i in a circular loop of radius b produces a magnetic field At a fixed point far from the loop on its axis the magnetic field is proportional to which of the following combinations of i and b A ib C i b B ib2 D i b

4 19 A neutral atom of atomic mass number 100 which is stationary at the origin in gravity free space emits an a particle A in z direction The product ion is P A uniform magnetic field exists in the x direction Disregard the electromagnetic interaction between A and P If the angle of rotation of A after radians what is n which A and P will meet for the first time is 25 the value of n A 12 C 36 B 24 D 48

A current of 10 A is flowing through a circular co of diameter 1 cm What is the magnetic induction at its centre O O O O 4 10 Tesla X 2 10 4 Tesla 4 x 10 10 8 Tesla 4 10 6 Tesla

17 A conducting rod with resistance r per unit length is moving inside a vertical magnetic field Bwith speed v on two smooth horizontal parallel ideal conducting rails The ends of the rails are connected to a resistor R the separation between the rails is d The rod maintains a tilted angle 0 to the rail Find the external force F required to keep the rod moving d a F c F V 0 B d v R dr B d v sine R dr sine B b F d F R B d v R dr sine B d v cos 0 R dr cos 0

For a circular coil of radius R and N turns carrying current I the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by B HIR 2N 3 2 2 x R a Show that this reduces to the familiar result for field at the centre of the coil b Consider two parallel co axial circular coils of equal radius R and number of turns N carrying equal currents in the same direction and separated by a distance R Show that the field on the axis around the mid point between the coils is uniform over a distance that is small as compared to R and is given by B 0 72 approximately HONI R

1 N and 2T 2 2N and T 3 2N and 2T 4 N and T A transformer of efficiency 90 has turns ratio 10 1 If the voltage across the primary is 220V and current in the primary is 0 5A then the current in secondary is 3 4 A 1 5 5 A 2 5 A 4 4 5 A Three particles start from the origin at the same time one with a velocity v along the x axis second along the negative y axis with v and the third particle moves along the line x y The

For the isolated charged conductor shown in figure The potentials at points A B C and D are VA VB Vc and Vp respectively Then B OVA VB VC VD OVD Vc VB VA OVD Vc VB VA VD Vc VB VA Marks 4

A particle is projected in a plane perpendicular a uniform magnetic field The area bounded by th path described by the particle is proportional to 1 The velocity 2 The momentum 3 The kinetic energy 4 All of these

Two long parallel metallic wires with a resistance R form a horizontal plane A conducting rod AB is on the wires shown in figure The space has magnetic field pointing vertically downwards The rod is given an initial velocity v There is no friction in the wires and the rod After a time t the velocity v of the rod will be such that A HP R B BLP Vo

An equilateral triangle of side a carries a current T Magnetic field at point P which is vertex of triangle 1 Mol 2 3 a 2 Hol 2 3 3 9 Ho 2 Hol O 4 2 Ho P a 1

203 A conducting ring rests on the top shown B At the moment shown the current is large but decreasing The magnetic force on the ring at this instant 1 Is zero 2 Has a component up and tries to expand the ring 3 Has a component up and tries to crush the ring 4 Has a component down and tries to expand the ring

A charge q is distributed uniformly on the surface of a sphere of radius R It is covered by a concentric hollow conducting sphere of radius 2R Charge on the outer surface of the hollow sphere will be if it is earthed 072 1 12 2 3 4g 2 2q 4 Zero

Two north poles each of pole strength m and a south pole of pole strength m are placed at the three corners of an equilateral triangle of side a The intensity of magnetic induction field strength at the centre of the triangle is 1 Ho m 4 a 2 Ho 6m 2 4 a

When we open the lid of a bottle by turning it our fingers are applying a couple to the lid Fig 7 21 a Another known example is a compass needle in the earth s magnetic field as shown in the Fig 7 21 b The earth s magnetic field exerts equal forces on the north and south poles The force on the North Pole is towards the north and the force on the South Pole is toward the south Except when the needle points in the north south direction the two forces do not have the same line of action Thus there is a couple acting on the needle due to the earth s magnetic field

Three wires of equal lengths are bent into the form of three loops One of the loops is square shaped second loop is triangular shaped and third loop is circular These are suspended in a uniform magnetic field and the same current is passed through them Which loop will experience greater torque Give reasons

Moving Charges and Magnetism 129 A charged particle enters a magnetic field at right angles to the magnetic field The field exists for a length equal to 1 5 times the radius of circular path of the particle The particle will be deviated from its path by 1 90 3 30 2 sin 4 180 G 3 MAGNETIC FIELD DUE TO A CURRENT ELEMENT BIOT SAVART LAW So far we have seen how a magnetic field applies force on a moving charge Here we shall study the relation between current and magnetic field it produces It is given by the Biot Savart law Figure shows a finite conductor XY carrying a current I Consider an infinitesimal element dl of the conductor The magnetic field dB due to this element is to be determined at a point P which is at a distance from it Let e be the angle between dl and the displacement vector r The direction of dl is same as the direction of current X

If a positively charged particle is moving as shown in the figure then it will get deflected due to magnetic field 1 towards y B q X 1 x direction 2 y direction 3 x direction 4 z direction 2 There is a magnetic field acting in a plane perpendicular to the sheet of paper downward into the paper as quum moves in the plane of paper from left to right as shown in figure The

A magnet of length 10 cm and magnetic moment 1 Am is placed along the side of an equilateral triangle of the side AB o length 10 cm The magnetic induction a third vertex Cis 1 10 9 T 2 10 T 3 10T 4 104T

2 Neutron 3 Electron 4 Alpha particle A charged particle is whirled in a horizontal circle by attaching it to a string fixed at one point If a magnetic field is switched on in the vertical direction the tension in the string 1 Will increase 2 Will decrease 3 Will remain the same 4 May increase or decrease New Delhi 110005 Ph 011 47623456

A particle having a charge of 10 C and mass 1 ug moves in a horizontal circle of radius 10 cm under the influence of a magnetic field of 0 1 T When the particle is at a point P a uniform electric field is switched on so that the particle starts moving along the tangent with uniform velocity The electric field is X 1 0 1 V m 2 1 0 V m 3 10 0 V m 4 100 V m A particle of charge 1 C is at rest in a magnetic field B 2K tesla Magnetic Lorentz force on the charge 10 A charged equal to 1 1 90 3 30 MAGNETIC F So far we between C Figure sho

5 A particle of charge 1 C is at rest in a magnetic field B 2k tesla Magnetic Lorentz force on the charge particle with respect to an observer moving with velocity v 51 m s will be 1 Zero 2 10 5 N 3 10 6 N 4 105N 6 A proton and an a particle enter a uniform magnetic field perpendicular with the same speed If proton takes Figure shows a The magnetic fi Let 0 be the an of current

vo particles of charges and 9 are projected from the same point with a velocity v in a region of uniform magnetic field B such that the velocity vector makes an angle masses are M and 2M respectively Then they will meet again for the first time at a point whose distance with the magnetic field Their from the point of projection is A 2 Mv os 0 QB B 8 Mv os 0 QB C TMv os 0 QB D T 4 Mv os 0 QB

Example 15 A jet plane is travelling west to east at a speed of 1800 km h What is the P D developed between the ends of the wing 25 m long if the earth s magnetic field at the location is of magnitude 5 0 104 T and dip angle is 30

6 Two straight conducting rod are connected by flexible conducting wires to form a rectangular outline g figure i The sides of the rectangle are a 30 cm and b 50 cm The circuit is placed in a uniform magnetic field with induction B 5 x 10 T directed perpendicular to the plane What is the charge Aq in C that flows along the contour if you turn it by 180 symmetrically as shown without the wires touching each other figure ii Loop resistance R 1 ohm Take self inductance of the system to be L 1 H Fill 150 in OMR sheet a Figumo b807 308A smsil ulus Ini mworia as oni sumse of Tubur beste o ni bossique tierbositus Ti of lennon raqsg Borli brun M42 zistiw of lo 25 Figure ii

A donut shaped permanent magnet magnetization parallel to the axis can slide frictionlessly on a vertical rod Treat the magnets as dipoles with mass m and dipole moment M When we put two back to back magnets on the rod the upper one will float At what height z does it float 1 3 2 0M 3 mag 71 4 3 0 M 71 4 2 m g Z 2 4 6 M mag HoM 6 mag 71 4 1 4

Magnetic field exist in the space and given as B Box k where Bo and are positive 1 constants A particle having positive charge q and mass m is projected with speed vo along positive x axis from the origin What is the maximum distance of the charged particle from the y axis before it turns back due to the magnetic field Ignore any interaction other than magnetic field A me vo 3qB C 1 3 1 3 3me vo 0 qBo A non conducting hollow cone has charge B D 3m vo 2qBo me vo qB 1 3 1 3

K The magnetic induction at the point O if the wire carries a current i is 1 2 3 4 Mol 2R Moi 2 R Moi 4 2 4TR Moi 4 y R O X

Read the following paragraph and give the answers to the questions Or 44 A current loop ABCD is held fixed on the plane of the paper as shown in the figure The arcs BC radius b and DA radius a of the loop are joined by two straight wires AB and CD A steady curren is flowing in the loop Angle made by AB and CD at the origin O is 30 Another straight thin wire with steady current I flowing out of the plane of the paper is kept at the origin i The magnitude of the magnetic field B due to arc AD at the origin O is A Zero HOI 24a C Hol D 4 ii The magnitude of the magnetic field B due to the arc BC at the origin O is 12 a B Hol b a B A Zero HOI 4 b iii The magnitude of the magnetic field B due to the loop ABCD at the origin O is 24b C Hol Hol D 12 b B Hol a b 24 ab C Hol b a 4 cb A 24 ab iv Due to the presence of the current I at the origin A The forces on AB and DCarc zero B The forces on AD and BC arc zero C The magnitude of the net force on the loop is given by D The magnitude of the net force on the loop is given by D Zero 1 2 a b a b 4x Holly b a 24ab