Magnetic Field Questions and Answers

Two particles having charge 2C and 1C are moving on a circle of radius 1m in the same direction with same speed v m s The magnetic field at the centre of the circle is value of v in m s is TU tesla Th

2 A conducting arm AB of length 30 cm moves on conducting rails held parallel A uniform magnetic field B 0 2 T exists perpendicular to planes of rails Only the conducting arm has resistance of 0 5 02 The arm is pulled out with constant speed of 20 ms how much force is required parallel to rails to keep it moving at same speed NCERT Pg 216 A 0 30 m OB Rail v 20 ms Rail

D A metallic rod of length 20 cm is rotated with frequency of 50 rev s with one end pivoted at the centre and other end at circumference of circular metallic ring of radius 20 cm about an axis passing through centre and perpendicular to plane of the ring A constant and uniform magnetic field 1 5 T parallel to axis is present everywhere What is emf induced between centre and periphery of circular ring INCERT Pg 214 2 9 4 V 4 12 3 V 1 2 6 V 3 4 7 V

A magnetic needle is placed in an external magnetic field at an angle 0 with the field Needle is in most stable position if the value of 0 is INCERT P178 1 180 3 0 2 90 4 60 certain place

A The moment of inertia of a solid cylinder about its own axis is the same as its moment of inertia about an axis passing through its one end and perpendicular to its length The relation between its length L and radius R is B C D L 2R L V R L 3R 4 00 L R 1 00

Two parallel long wires carry currents it and 12 with i i2 When the currents are in same direction the magnetic field at a point midway between the wires is 40 T If the direction of it is reversed the field becomes 60 T The ratio iia is 1 1 6 3 5 1 2 1 5 4 6 1

A conducting sphere of radius R is placed in a uniform electric field Edirected along z axis The electric potential for outside points is given as V Qut ET 1 25 r cos 0 wherer is the distance from the centre and is the polar angle The charge density on the surface of the sphere is a 380 E cos 0 b E Ecos c 380 E cos d 3 Eo cose

A plane electromagnetic wave of frequency w is incident on an air dielectric interface The dielectric is linear isotropic non magnetic and its refractive index is n The reflectance R and transmittance 7 from the inter face are a R n c R T 3 n 4n n 1 47 n 1 T 1 1 n b R d R n 1 n l T 2 n 1 41 n 1 T

A circular arc QTS is kept in an external magnetic field B as shown in figure The arc carries a current I The magnetic field is directed normal and into the page The force acting on the arc is Y a 21 BOR B x xx T x x x x XXX 1 X X X X X X X X X X X X X X X X X b I BORJ XX c 21 BOR d I BRI

A hollow thin walled conducting long cylinder of radius R is carrying current along its length A thin slit of width h is cut along the length of cylinder The magnetic field just inside the cylinder at the points near the slit is h R Hol 2R Ho 2zh Hol 2 R

viii Figure 4 134 shows a horizontal wire MN of length and mass m is placed in a magnetic field B The ends of wire are bent and dipped in two bowls containing Hg which are connected to an external circuit as shown If key is pressed for a short time St due to which a charge q suddenly flows in the circuit Find the maximum height above initial level the wire MN it will jump X LIE X M X X Hg X Hg Figure 4 134 THE F N St X

An electron travels with speed 5 0 106 m s between the two parallel charged plates shown in the figure The plates are separated by 1 0 cm and are charged by a 200 V battery Figure 1 gure 1 of 1 V 1 0 cm Part A What magnetic field strength will allow the electron to pass between the plates without being deflected Express your answer using two significant figures VAE B Submit Part B Request Answer What is the direction of the magnetic field O Up O Down O Out of the page O Into the page T

vii A square frame with side a and a long straight wire carrying a current i are located in the same plane as shown in figure 5 51 The frame translates to the right with a constant velocity v Find the EMF induced in the frame as a function of distance x Hoia xv 2r r a 1 1 Figure 5 51

1 A toroid ring has inner radius 21 cm and outer radius 23 cm in which 4400 turns of wire are wound If the current in the wire is 10 A then magnetic field inside the core of the toroid will be NCERT Pg 170 1 4 4 x 10 4T 2 4 x 10 2 T 3 6 6 x 10 4T 4 12 6 x 10 T

5 52 A square loop of area 2 5 x 10 m and having 100 turns with a total resistance of 10002 is moved out of a uniform magnetic field of 0 40 T in 1 sec with a constant speed Then work done in pulling the loop is A zero C 1 J X X 1 Figure 5 306 B 1mJ D 0 1 mJ

4 34 Figure given in the question is a cross sectional view of a coaxial cable The centre conductor is surrounded by a rubber layer which is surrounded by an outer conductor which is surrounded by another rubber layer The current in the inner conductor is 1 0A out of the page and the current in the outer conductor is 3 0A into the page Determine the magnitude and direction of the magnetic field at points a and b 3A IA a 1mm Immlmm Figure 4 260 b Ans 200 T toward the top of the page 133 T toward the bottom of the page S

4 44 A proton of charge e and mass m enters a uniform magnetic field B B with an initial velocity v vi v Find an expression in unit vector notation for its velocity at time t V Be Ans v vi v cos cof v sin ootk Here oo m

A square frame of resistance en 2 and side a 20 cm and a long straight infinite wire carrying a current I 10 amp are located in the same plane as shown in figure The frame is rotated through an angle of 120 about the side PQ as shown The amount of charge flown through the loop during this time is q x 10 7 coulomb find the value q I a a

4 54 The magnetic induction due to a current carrying circular Moop of radius 3m at a point on the axis at a distance of 4m from the centre is 54 T What will be its value at the centre of the loop A 250 T V C 125 T B 150 T D 75 T

A loop shown in the figure 5 311 is immers Narying magnetic field B Bot directed into the page If the total resistance of the loop is R then the direction anc magnitude of induced current in the inner circle is b G X B Figure 5 311 A Clockwise Bo na b R B Anticlockwise Bot a b R C Clockwise Bo ra 4b R D Clockwise Bo 46 na

In this sum they have asked to find magnitude and directi on of magnetic field at point P Why have they taken cos here instead of sin Sol i 4a i 4a Bp BD 0 ABA Magnetic field at point P Hoi 4 a 5a 3a 3a cos 0 cos 0 Hoi 4 3a From the figure PA 3a 4a PA 25a 4 From the figure cos 0 5 cos 0 cos 0 PA 5a f the Hoi 6 Cos 0

If a semicircular conducting loop ACB is rotating in the plane of paper with constant angular velocity w about O then which of the following graphs shows the variation of induced current with time t The magnetic field is perpendicular to the plane of loop as shown in the figure 100 O X X X X X X X X X X X X X X X X X X X X X D

28 A beam of protons with a velocity 4 x 105 m s enters a uniform magnetic field of 0 3 T at an angle of 60 to the magnetic field Find the radius of the helical path taken by the protons beam Also find the pitch of the helix which is the distance travelled by a proton in the beam parallel to the magnetic field during one period of rotation 1986 6M

V A light rod of length L is hanging from the vertical smooth wall of a vehicle moving with acceleration 3 g having a small mass attached at it s one end is free to rotate about an axis passing through the other end The minimum velocity given to the mass at it s equilibrium position so that it can complete vertical circular motion is KgL Find the value of K

A bullet of mass 15g travelling horizontally with a velocity of 150 m s strikes a stationary wooden block and comes to rest in 0 03 seconds The distance of penetration of the bullet into the block will be Options 2 60m 7 75 m 5 0 m 2 25m

0 In a uniform magnetic field an alpha particle is rotating in a circle of radius R with kinetic energy K If a deuteron has to rotate in the same circle then its kinetic energy will be 1 K 3 2K 2 K2 K2 4

2 A solenoid of diameter 0 2 m has 500 turns per metre At the centre of this solenoid a coil of 100 turns is wrapped closely around it If the current in solenoid changes from zero to 2 A in 1 millisecond Induced emf developed in the coi is nearly 1 2 45 V 3 6 55 V 2 3 95 V 4 1 25 V

Find the volume of the region enclosed by the solid right circular cylinder whose base is the region in the xy plane that lies inside the cardioid r 1 cos 0 and outside the circle r 1 and whose top lies in the plane z 4

The ratio of the magnetic field at the centre of a current carrying circular wire and the magnetic field at the centre of a square coil made from the same length of wire will be 2 1 4 3 3 TC 2 2 C 2 8 2 T 4 4 2

A square of conducting loop of side length L carries a current I The magnetic field at the centre of the loop IS A independent of L C inversely proportional to L E Proportional to L B proportional to L D linearly proportional to L

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How many neutral points will be obtained when bar magnet is kept with magnetic moment paral to earth s magnetic field 1 One 3 Four 2 Two 4 Infinite

Q A circular loop of radius 0 3 cm lies parallel to a much biger circular loop of radius 20 cm The centre of the small loop is on the axis of the axis of the bigger loop The distance between theri centres is 15 cm If a current of 2 0 A flows through the smaller loop then the flux linked with bigger loop is JEE Main 2013 a 6 10 11 weber b 3 3 10 11 weber c 6 6 10 9 weber d 9 1 10 11 weber X

A horseshoe magnet is placed around a current carrying straight wire as shown in figure Force on the wire is vertically upwards then A is 1 South pole 2 North pole 3 South pole or North pole 4 Not a magnet Current force is up A U

A track consists of two rough planes forming an angle 90 with each other It is symmetric to vertical axis and makes an angle 37 with the horizontal Coefficient of friction of the planes are different and are 1 plane and u for right plane A cube is released from rest as shown such that it s two faces rest on the given planes Find it s acceleration 2 2 10 37 NT for

created by 1 Super conductor 3 Both 1 2 2 Soft iron ring 4 Neither 1 no

men are running in a line along a road with velocity 9 km hr behind one another at equal intervals of 20m Cyclist are also riding along the same line in the same direction at 18 km hr at equal intervals of 30m The speed with which an observe must travel along the road in opposite direction so that whenever he meets a runner he also meet a cyclist is A 9 km h B 12 km h C 18 km h D 6 km h

The The figure shows a part of an resistances The separation between the wires AB CD and EF are long and have identical neighbouring wires is 1 0 cm The wires AE and BF have negligible resistance and the ammeter reads 30 A Calculate the magnetic force per unit length of AB and CD A A B D

A vertical conducting ring of radius R falls vertically in horizontal uniform magnetic field of magnitude B The direction of B is perpendicular to plane inward When speed of ring is v 20 A OB D 1 Current flows in the ring 2 A and D are at the same potential 3 C and E are different potential 4 The potential difference between A and D is oppy

A conducting ring of radius r X X X X is rolling without slipping with a constant angular velocity X XX0 figure If the magnetic field XxxxxPX strength is B and is directed into XXXXXX the page then the emf induced across PQ is X XOX X X a Bwr c 4Bwr b d X 2 Bwr 2 r Bw 8 X X X

A positively charged particle specific charge m is projected in xy plane with speed 4 m s in a gravity free space having uniform electric field E E Uniform magnetic field B Boj is also switched on in the space at t 0 when speed of charged particle is minimum During motion of charged particle if is Bo maximum possible z coordinate of the particle then value of k is Z 60 v 4 m s

p Let B B and B be the magnetic fields produced by the three infinite long wires P Q and R respectively These wires are placed symmetrically inside an equilateral triangular loop as shown in the figure A B of I is a 15 A b 5 A c 13 A K 31 3a 31 RO B Current in 3 wires are as shown in figure If B di 44 and Bodi 15 Considering SI units the value A

2 96500 25 How long has a current of 3 ampere to be applied through gh a solution of silver nitrate to coat a metal surface of 5 cm with 0 005 mm thick layer Density of silver is

In the given figure an electron enters into the uniform magnetic field It deflect in the direction y x ex X X X X X X X ve x direction ve x direction ve y direction ve y direction X

Figure shows two concentric charged metalic spherical shells A and B Electric potential on the surfaces of A and B are V and V respectively If they are connected by a conducting wire then electric potential on the surface of B will be A B BA XOX Xv KA FOX 2R 12V B 6CMC

ar magnet in vibration magnetometer makes 30 oscillations per minute where the horizontal component of magnetic field is 9 x 10 5 T The izontal magnetic field at a place where the magnet makes 20 oscillations per minute is 4x10 5 T 8x 10 5T O 2x 10 5 T O 105 T

A short magnet stays in stable equilibrium in a uniform magnetic field The work required to rotate it by 30 is K The torque required to hold the magne in this position is OK K 3 OK 2 3 O K 2 3

A magnetised wire bent at 60 at its mid point has a dipole moment M If it is stretched such that the angle becomes 90 at the mid point then its new dipole moment will be O2M O M 2 O 3M 2 O 2M 3

Two short magnets each of dipole moment m are kept perpendicular to each other joining their centres The magnetic field intensity at a distance R from the centre of the magnets on the axis of one of the magnets is O O Ho m 4x R Ho 2m 4x R Ho 3m 4x R Ho 5m 4 R

A long straight wire that has a circular loop with a radius of 0 05m it is given that the current flowing through this closed circular loop is 2 A Determine the magnetic field of this long straight wire