Magnetic Field Questions and Answers

A conducting rim of radius R rolls without slipping on a horizontal surface The speed of the ring s centre of mass is Up A uniform magnetic field B perpendicular to the ring s plane is swithched on The emf induced across point of contact and the topmost point of the rim is 2Bvo R X A X X X X B EX X X o

A hypothetical magnetic field existing in a region is given by B Boer where er denotes the unit vector along the radial direction A circular loop of radius a carrying a current i is placed with its plane parallel to X Y plane and the centre at 0 0 d Find the magnitude of the magnetic force acting on the loop A B C D i2ba a d4 i2d a Va b ba a d i2 b a Va d Correct Answer

A neutron beam of initial kinetic energy E is divided into two beams at point O by some mechanism Thereafter the beams proceed on the path OAC and OBC without a phase change at the corners A and B to interfere with each other at point C Here OACB is a square of side 1 tilted at an angle above the horizontal Mass of the neutron is m Planck s constant is h and acceleration of free fall is g the possible expression s for angle 8 at which a Maxima is detected at C is are 2hl2mE h A sin thi 1 2m gl C sin 6hl 2mE 2m gl 9h D A Horizontal B sin D tan 2hl 2mE m gl 2h m gl 2h1 2mE h 2m gl

In any experiment to measure ratio of radii of circular paths Two particles having charge 2q and q are projected with same speed v If the masses of particles are m and 2m respectively If these particles are projected perpendicularly in uniform magnetic fiel B then ratio of radii of their circular paths will be O 112 114 01 3

the first important machine for producing high energy electrons The action of the betatron depends on the same fundamental principle as that of the transformer in which an alternating current applied to a primary coil induces an alternating current usually with higher or lower voltage in the secondary coil In the betatron secondary coll is replaced by a doughnut shaped vacuum chamber Electron produced in the doughnut from a hot filament are given a preliminary acceleration by the application of an electric field having potential difference of 20 kV to 70 kV when an alternating magnetic field is applied parallel to the axis of the tube two effects are produced 1 an electromotive force is produced in the electron orbit by the changing magnetic flux that gives an additional energy to the electrons 2 a radial force is produced by the action of magnetic field whose direction is perpendicular to the electron velocity which keeps the electron moving in a circular path Conditions are arranged such REVIEW BOOKLET 2021 JLLA PART IL PHYSICS that the increasing magnetic field keeps the electron in a circular orbit of constant radius The mathematical relation between the betatron parameters and electron parameters to ensure the above condition is called BETATRON condition If the orbit radius of the circular path traced by the electron is R magnetic field is B speed of the electron is v mass of the electron is m charge on the electron is o and is the flux within the orbit of radius R Then answer the following questions based on the above comprehension 7 8 MEGACOSM 9 What is the tangential force acting on the electron A evB e de 2 R di What is the value of dB G A eR C e do 2nR dt What is the BETATRON condition e do R dt A BeV de d C dt dt dimlv dit R B B D B Bev D e de RR dt ev R B ev R do dt dit D Data insufficient to determine 2 R 8

A particle of mass m is constrained to move in one dimension under a potential u x a B where x X a and are positive constants Show that period of small oscillations about the equilibrium point is T 45 20 2a m

Q 24 Figure shows a square loop 20 cm on each side in the x y plane with its centre at the origin The loop carries a current of 7 A Above it at y 0 z 12 cm is an infinitely long wire parallel to the x axis carrying a current of 10 A The net force on the loop is 10 N ielliteo A than AZ D non BET d X y C

A charged particle is projected an angle 8 in uniform magnetic field with speed v After time t its speed will be O v sine O v cose Ov O Zero

A solid cylindrical wire of radius R carries current distributed uniforml over its cross section The magnetic field at a distance from the axis of the wire will be 2 O O Hol 2TR Ho 4x R Hol TR Mol 2R

F q UxB qvx Bi Bj Bok For q 1 and v 2 i 4j 6k and A F 4i 20j 12k What will be the complete expression for B 1 6i 6j 8k 2 3 8i 8j 6k 6i 6j 8k

Two conducting circular loops of radii R and R are placed in the same plane with their centres coinciding If R R the mutual inductance M between them will be directly proportional to 1 2 3 4 R2 2 R R R2 R2 R R F

41 An electric dipole is placed in a uniform electric field The net electric force on the dipole A Is always zero B Depends on the relative orientation of the dipole and the field C Can never be zero D Depends on the strength of the dipole

P 1 2 3 An infinitely long straight conductor carries current of 5 A as shown An electron is moving with a speed of 105 m s parallel to the conductor The perpendicular distance between the electron and the conductor is 20 cm at an instant Calculate the magnitude of the force experienced by the electron at that instant Electron v 105 m s 20 cm 5 A Q 4TX 10 20 N 8 10 20 N 4 10 20 N 8TX 10 20 N

A charge particle q m is released from rest in gravitational field Just when it is about to fall a uniform magnetic field Bo is switched on Maximum speed acquired by the particle during its motion is nmg qBo Find n X x X x X X X

having equal turns and carrying equal currents in same sense are placed co axially such that they subtend the same solid angle at O Let B be the magnetic field at O due to smaller coil X then 2r X Y 1 Magnetic field at O due to larger coil 2B B 2 2 Magnetic field at O due to larger coil 3 Total magnetic field at O is 4 Total magnetic field at O is 3B 2 O 5B 2

whether to add or subtract Please solve this problem Try Yourself 10 What is net magnetic field at point O 1 2r ii iv R O 2

17 A current of 2A is flowing in 2 points the sides of an equilateral triangle of side 2x10 2 m The magnetic field at the centroid of the triangle is OA 4x10 5 T OB 6x10 3 T O C 6x10 9 T OD 8x10 5 T

X 16 A rectangular coil of length 0 12m and width 0 1 m having 50 turns of wire is suspended vetically in a uniform magnetic field of strength 0 2 Wb sq m The coil carries a current of 2A If the plane of the coil is inclined at an angle of 30 with the direction of the field the torque required to keep the coil in stable equilibrium will be A 0 12 Nm B 0 15 Nm 0 2 X

A charge particle q m is projected from origin at t 0 with velocity v making an angle of 37 with x axis in x y plane A uniform magnetic field Boi exists in the m region Find the distance of the particle from origin at t qB O O O 4mvo 5qBo 3mv 2 9 5q80 mvo qBo 2mvo 4 9 5qBo 4 60 11 16 21 26 31 36 41 46 51

Shown below is a wire carrying current in upward direction What will be direction of magnetic field at position A as shown Use the direction indicator as shown A Towards North B Towards East C Towards West D Towards South E None of the above Q1 OPTIONS A B C Direction of ERNE D B E North East

if magnetic field lines can pass through a conductor then why dont they pass through soft iron ring is it bcoz of its material or bcoz of its shape a B lines can pass through a conductor However when a soft iron ring is placed in magnetic field no lines pass through the space inside the ring This phenomenon is called magnetic screening or Shielding and is used to protect costly wrist watches and other sensitive instruments from external magnetic fields Also know that the B field inside superconductors is always zero if kept in external B field This effect is known as Meissner Effect

Q H A In a region of space a uniform static magnetic field of induction B is established above the x z plane and another uniform static magnetic field of induction B B is established below the x z plane Both the fields are in the positive 2 direction A particle of mass m and charge q is projected from the origin with velocity v making an angle with x axis as shown in the figure Find average velocity of the particle in a large time interval U 0

Two large metal sheets carrying surface currents as shown in the figu The current through a strip of width dl is kdl where k 5 0 A m The magnetic field at point P will be P x 10 6 T towards left x 10 6 T towards right 2 x 10 6 T towards left 2 x 10 6 T towards right

A square loop ABCD carrying a current of 5 0 A is placed near a long wire carrying 100 A current as shown in the figure The loop and the wi are in same plane The magnitude of the magnetic force on the loop is 100 A 1 cm B A O 2 5 x 10 5 N O 5 x 10 5 N 1 5 10 5 N 10 x 10 3 N 5 A 1 cm C

Two charged particles M and N enter a space of uniform magnetic field with same velocities perpendicular to the magnetic field The paths are as shown in figure Then X X X X N V x X Charge of Mis greater than that of N The momentum of Mis greater than that of N Specific charge of Mis greater than that of N

A magnet makes 40 oscillations per minute at a place having magnetic field induction of 0 1 x 105 T At another place it takes 2 5 s to complete one vibration The value of earth s horizontal field at that place is

A charged particle is projected in a space where electric field E Eoi and B Boj is present If particle is projected with velocity v vok E voBo then Particle move on a circular path Particle move on a straight line path Particle move on a parabolic path hr mir Particle move on a helical path

Two charged particles moving with same velocity traverse identical helical path in a completely opposite sense in a uniform magnetic field B Bok They have equal mass They must have equal charge They necessarily represent a particle and antiparticle pair The charge to mass ratio satisfy e e m 1 m 2 0

na circular wire of radius R a battery of voltage Vo is applied across point A and B If resistance of circular wire is 160 then B Current through battery is Current through battery is 20 O Magnetic field at centre O due to current in circular wire is zero

Two protons move parallel to each other with speed v and v Net force between them Attractive O Repulsive Not any force between them None of these

Two current carrying loops of radius R and 2R carrying current and 2 respectively are placed concentrically with their planes at right angle If magnitude of resultant magnetic field at the centre Ho 2R is N then value of N is 5

8 Two charged particles having the same mass m and charges q and q separated by a distance d enter a uniform magnetic field B directed perpendicular to the paper inward with speeds v and v as shown The particles will not collide if neglect electrostatic force between charges d 10v 2m 1 d v V dz Bq 2m 3 d v V Ba X X X X X X X X 2 d 2m qB V V 2m 4 d v V

A particle of charge q and mass m starts moving from the origin under the action of an electric field E E 1 and B Boi with a velocity v uoj the speed of the particle will become after a time mvo qE mvo 2qE 3mvo 2qE 5vo 2

17 A charged particle of specific charge a m released from origin at t 0 with velocity v i 1 V Voi i in uniform magnetic field Coordinates of particle at time t Vo 210 Yo 1 2B a aB Ba 2 2v VOT 2V0 2 A TL B a B B 1 are is Vo 0 0 2B Vor 2vo 0

A time varying voltage V 2t Volt is applied across an ideal inductor of inductance L 2H as shown in figure Then 2H 666666 V 2t d current versus time graph is a parabola Benergy stored in magnetic field at t 2 s is 4J potential energy at time t 1 s in magnetic field is increasing at a rate of 1 J s

A charged particle entering in a magnetic field from outside in a direction perpendicular to the field X Will always complete exactly half of a rotation before leaving the field Can never complete one rotation inside the field May or may not complete one rotation in the field depending on its angle of entry into the field All of these

A charged particle is projected with velocity voi in combined uniform electric field E and uniform magnetic field B Column Il gives the possible path of particle corresponding to condition in Column l Match the entries in Column l with entries in Column II Column l Q1 E 0 B 0 Q2 0 B 0 Q3 E 0 B 0 Q4 E 0 B 0 Q1 Q2 Q3 A1 A2 A3 A4 A5 Column II A1 Straight line A2 Parabola A3 Helix A4 Circle A5 Cycloid

A beam of protons with a velocity 4 x 105 m s enters a uniform magnetic field of 0 3 tesla at an angle 60 to the magnetic field Find the pitch of the helix in centimeters which is the distance travelled by a proton in the beam parallel to the magnetic field during one period of rotation Mass of the proton 1 67 x 10 27 kg

A particle of charge 1 C is at rest in a magnetic field 2 tesla Magnetic Lorentz force on the charge particle with respect to an observer moving with velocity 51 ms will be Zero 10 IN 10 IN 10 IN

4 48 A coil with magnetic moment 1 45A m is oriented initially with its magnetic moment antiparallel to a uniform 0 835T magnetic field What is the change in potential energy of the coil when it is rotated 180 so that its magnetic moment is parallel to the field

An elastic circular wire of length carries a current I It is placed in a uniform magnetic field B Out of paper such that its plane is perpendicular to the direction of B The wire will experience OB OF 1 Question Type Single Correct Type 2 13 3 No force B A stretching force A compressive force

Two short magnets of equal dipole moments M are fastened perpendicularly at their centres shown in figure The magnitude of the magnetic field at a distance d from the centre on the bisector of the right angle is N 1 S N P S Question Type Single Correct Type 2 Ho M 4 d d Ho 2M 4

toroid 25 A solenoid of length I has N turns of wire closely spaced each turn carrying a current i If R is cross sectional radius of the solenoid the magnetic induction at P only axial component 1 AN HoiN 2 R 1 HoiN 2 121 1 XXXXXXXX 1 2 0 O 1 2 0 P X

20 A horizontal overhead power line is at a he of 4m from the ground and carries a current 100 A from east to west The magnetic field dire below it on the ground is 4x107TmA 1 2 5 x 107T southward 2 5 x 106 T northward 3 5 x 106 T southward 4 2 5 x 107 T northward

tive y axis A current I flows along an infinitely long straight thin walled tube of radius R The magnetic field at a point inside the tube at a R distance from the wall is 2

A current element 0 00 im is placed at the origin and carries a large current of 10A Then the magnetic field due to this current element at a distance 0 4 m on the y axis is 1 6 25 x 109 kT 2 1 25 x 10 8 kT 3 6 25 x 109 iT 4 1 25 x 108 iT

A thin flexible wire of length L is connected to two adjacent fixed points carries a current I in the clockwise direction as shown in the figure When system is put in a uniform magnetic field of strength B going into the plane of paper the wire takes the shape of a circle The tension in the wire is C 1 IBL uestion Type Single Correct Type 2 X X X IBL X X X X XXXX X X X X X X X X X X X X X X X X X

24 A conductor ABOCD moves along its bisector with a velocity 1 m s through a perpendicular magnetic field of 1 wb m as shown in figure If all the four sides are 1 m length each then the induced emf between A and D in approx is V

A disc of radius R having uniform charge Q is rotated about its axis with angular speed w The magnetic moment is RAYA 314 Ga Medium Current Loop As A Magnetic Dipole Single Choice A B C QoR 2 QoR 4 Qo R 5 27 W

Which of the following correctly describes the magnetic field of a long straight wire 1 The field consists of straight lines perpendicular to the wire 2 The field consists of straight lines parallel to the wire 3 The field consists of radial lines originating from the wire 4 The field consists of concentric circles centred on the wire