Magnetic Field Questions and Answers

A current carrying wire is bent to form a circular coil If this coil is placed in any other magnetic field then for maximum torque on the coil the number of turns will be 1 1 2 2 3 4 4 8

A wire carrying a current i is placed in a uniform magnetic field in the form of the curve y a sin 7 0 x 2L The force acting on the wire is y 1 iBL T 2 iBL 3 2iBL 0x X X X X X X X X X XX X X X X X X X B X 2L X X X X X X X X

A student connects a wire to a battery and notices a nearby compass turns toward the wire What conclusion can the student draw from this observation O a Compasses produce a magnetic field b Compasses produce electric current Oc Magnetic fields produce electric current d Electric current produces a magnetic field

A straight wire of length 10cm is bent into a circular arc of radius 2 5 cm and made to carry a current of 5 A The magnetic field at centre of the arc of the circle is A 0 8G B 1 6G C 0 4G D 2 4G

Which of the following statement is wrong regarding A C generator A When flux through coil is maximum emf induced is minimum B No emf is induced when plane of coil is parallel to magnetic field C The emf induced changes periodically with time if coil is rotated at uniform rate D The frequency of rotation armature coil is 50 Hz in India and 60 Hz in USA

A rod of length 20 cm is rotating with angular speed of 100 rev per sec in a magnetic field of strength 0 5 T about it s one end What is the potential difference between two ends of the rod Question Type Single Correct Type 1 2 28 V 2 4 28 V 3 6 28 V

3 A magnet is placed in a non uniform magnetic field It experiences a a force but not a torque b a torque but not a force c a force and a torque d neither a force nor a torque AMU Med 2010 BHU 2009

A balloon of mass Mis ascending at constant acceleration a When mass m is added to balloon it starts descending with acceleration a Assuming its volume does not change find the value of m 20 g a M 20 2 g 20 20 Ma 20 g M C

62 Two straight infinitely long current are kept along Z axis at the coordinates 0 a 0 and 0 a 0 respectively as shown in the figure The current in each of the wire is equal and along negative Z axis into the plane of the paper Y a c B a The variation of magnetic field on the X axis will b approximately B X a X 8 Z b B B X

9 abcd is a square There is a current I in wire efg as shown b e Choose the correct options a Net magnetic field at a is inwards c Net magnetic field at cis outwards a f C 1 1 1 1 19 d b Net magnetic field at b is zero d Net magnetic field at d is inwards

Q 1 Two long straight wires carrying current in the positive z direction cross the xy plane at 0 3 0 and 0 3 0 The magnetic field at the point 4 0 0 is B x 10 7 Tesla What is the closest value of B Max score 1 Neg score 0 5 2 2 6 0 04

Q 3 Two long conductors have electrostatic charge per unit length A They lie parallel to the x axis at a distance d Now both are given a constant speed V along the x axis What is the magnitude of the magnetic force per unit length on one of the conductors due to the other Max score 1 Neg score 0 M1 12 4 d M1 12 2nd 201 12 d

Two identical ring of equal mass m and radius R rigidly attached wears a bead of mass m Bead can freely slide without friction It is hinged at point P in such a way that it can freely rotates about horizontal axis passing through point P The ring and bead are released from rest from give position Then just after release A The magnitude of angular acceleration of ring is 2g B The magnitude of angular acceleration of rod is 9R C The magnitude of acceleration of bead is 5g 17R D The magnitude of acceleration of bead is 2g 7 858 e

A uniformly rigid ring of radius r and unknown mass is placed on a nonconducting frictionless horizontal table where exists a uniform magnetic field of induction B as shown A current I that is double of the minimum current required to flip over the ring is made to circulate in the coil Find the force of normal reaction from the tabletop on the ring immediately after the current is switched on 5 rl 6 Option 1 B 5 r IB 3 O Option 2

46 A small square loop of wires of side b is placed inside a large square loop of wire of side a b as shown in figure the loops are coplanar and their centres coincide The mutual inductance of the system is proportional to gruoropples botoe Depu W 19 a bropea d 0092 6 ilim 2 101 18 is gool srit ni 1 V 80 0 S V 40 0 5 V 80 0 A 15V ano tuodis esistor gonstalasi bris I niggel to bon A nb re as bre ona naibuhoon sobre rodio 211 epi 2 1 a

1 2 12 x 10 5 m s 3 1 56 x 10 5 m s 2 0 78 x 10 5 m s 4 none of these There is a current of 40 amperes in a wire of 106 m area of cross section If the number of free electrons per m is 1029 then the drift velocity will be 1 1 25 x 10 m s 2 2 50 10 m s 3 25 0 x 10 m s 4 250 x 10 m s S I unit of current is 1 C

Two co planar concentric circular coils of radii a and b are placed in the y z plane such that the common center of the coils is origin a b A current i flows in the outer coil Now the inner coil is moved along the x axis with a constant speed v keeping its plane unchanged The emf induced in the inner coil is maximum at A a V B 3a V C D t 4 t a 2v

A particle having of 5 x 10 C The particle is given an initial I JA LIJ 8 horizontal velocity of 105 ms in the presence of M60 9viw idols de aral s brs st w to appl shipp electric field E and magnetic field B To keep the bas etnome 9Tugit ni nworle en vlovitoegest particle moving in a horizontal direction it is ambe 90 ar b9opiq 916 929ril 16dt grimuzzA necessary that etingo orth is ones ad liw ableit onongamodT 9n6lq 21 H notisqe sdi nadw gool art to a B should be perpendicular to the direction of Stw velocity and E should be along the direction of velocity S b Both B and E should be along the direction of velocity AI 8 c Both Band E are mutually perpendicular and perpendicular to the direction of velocity d B should be along the direction of velocity and bisit ottengsm motinu s to sonsultni edt 19bn E auibot to should be perpendicular to the direction I ril to boneq velocity mut orT v bosqe instano rliiw Which one of the following pairs of statements is possible no ton bns A no abnoqsb I no jon brs v no abroqob S 1 c and d brus drog 2 b and c

Spacecraft Alpha is moving at 0 90c with respect to the earth If spacecraft Beta is to pass Alpha at a relative speed of 0 50c in the same direction what speed must Beta have with respect to the earth

Wo identical electric point dipoles have dipole moments p pi and p pi and are held on the xaxis at distance a from each other When released they move along the x axis with the direction of their dipole moments remaining unchanged If the mass of each dipole is m their speed when they are infinitely far apart is A B P 3 a2 ma 1 a 2 ma

6 Magnetic field in a cylindrical region is given by B at A positive charge q of mass m is projected from point P as shown RO P The de Broglie wavelength of the charge 1 Increases 2 Decreases 3 Remains unchanged sil bail 4 Remains unchanged irrespective of direction of projection rftod not hal

1 x A positively charged particle having charge q 1C and H 40cm mass m 40g is revolving along a circle of radius R with velocity v 5m s in a uniform magnetic field with centre of circle at origin O of a three dimensional system At t 0 the particle was at 0 0 4m 0 and velocity was directed along positive X direction Another particle having charge q 1C and mass m 10g moving uniformly parallel to Z direction with velocity v 40 n m s collides with revolving particle at t 0 and gets stuck to it Neglecting gravitational force and coulomb force calculate x y and z coordinates of the combined particle at t 40s 0 2m 0 2m 0 2m

An infinite wire placed along z axis has current I in positive z direction A conducting rod PQ placed in xy plane parallel to y axis has current I in positive y direction The ends of the rod subtend angles 30 and 60 at the origin with positive x direction as shown in figure 4 115 The rod is at a distance a from the origin Find net force on the rod y 30 60 1 Q

A coil of 50 turns and 10cm diameter is made out of a wire of resistivity 2 x 10 6 cm and cross sectional radius 0 1mm The coil is connected to a source of EMF 10V and of negligible internal resistance a Find the current through the coil b What must be potential difference across the coil so as to nullify the horizontal component of earth s magnetic field 0 314 10 T at the centre of the coil How should the coil be placed to achieve this result a 1A b 0 5V coil is placed in a plane normal to magnetic meridian dis def 60 in I

viii A magnetic needle performs 20 oscillations per minute in a horizontal plane If the angle of dip be 30 then how many oscillations per minute will this needle perform in vertical north south plane and in vertical east west plane 21 5 min 15 2 min

2 Given two diagrams of current carrying 3D loops along some sides of a cube If B B are the magnitudes of net magnetic ield at point P in diagram A and diagram B respectively Which of the following option s is are correct Same current n both loops a O 2b B B B B B B 2b B and B are anti parallel 2 P

A proton mass 1 673 x 10 27 kg moves with an initial velocity 1 87 15 04 0 km s at the origin in a uniform magneti field B 21 99 0 0 mT To an observer on the negative x axis the proton appears to spiral in the counter clockwise O clockwise The radius of this circular motion is mm

y 4 O X A tightly wound thin wire semi infinite solenoid of radius R and n turns per unit length carries a current I Magnetic field well inside the solenoid is uniform but near the end it fans out Find the magnetic induction vector B in terms of radial and axial components at a point outside the solenoid and at a distance x from the end and a very small distance r from the axis You may denote unit vector in the positive x direction by and unit vector away from the x axis in y z plane radial direction by

A subatomic particle with charge q 35 C is injected into a magnetic field B 8 T pointing into the page with a velocity of 0 6 m s It curves to the left and is detected at point A at a distance d 30 cm from the opening a What is the particle s mass b Is the particle positive or negatively charged

B 6 A charge particle starts sliding down a frictionless slope of inclination in presence of a horizontal uniform and static magnetic field of induction B directed perpendicularly into the plane of the figure and uniform gravitational field of the earth Intensity of the gravitational field is g After sliding an unknown distance 1 the particle leaves the slope and follows a cycloidal trajectory as shown in the figure If on the trajectory maximum vertical displacement of the particle is h find the distance l it had slid on the slope

hree long straight wires are seen end on as shown in the figure The distance between the wires is r 0 240 m Each carries current IA IB Ic 1 91 A Assume the only forces exerted on wire B are due to wires A and C Find the magnetic force per unit length kerted on wire B Express your answer in vector form B net N m A X

subjected to loads at points P Q R and S as shown in the figure below 200 N P Q 400 N a 5 m c 20 m 300 N R S 500 mm 1000 mm 500 mm If Esteel 200 GPa the total change in length of the rod due to loading is b 10 m d 25 m 100 N ESE 2016

An infinitely long straight conductor is bent into the shape as shown below in fig It carries a current of i ampere and the radius of the circular loop is r metre Then the magnetic induction at the centre of the circular part is 1 zero H2i goist so BF Brut Biy 57 B B 40 BAY 2 infinite Ho 2i

2 63 Collar A is connected as shown to a 50 lb load and can slide on a frictionless horizontal rod Determine the magnitude of the force F required to maintain the equilibrium of the collar when a x 4 5 in b x 15 in P 1 B 50 lb 20 in

XR and X are respectively the rms and average values of x t x t T and similarly YR and YA are respectively the rms and average values of y t kx t k T are independent of t Which of the following is true

A current I flows through a thin wire shaped as regular plygon of n sides which can be inscribed in a circle of radius R The magnetic field induction at the centre of polygon due to one side of the polygon is 2 HI 4TR tan n TR 11 A coil of inductive reactance 3 H1 2x R tan n 4 cos n 2TR 31 o has a resistance of 80 It is placed in series with a

A neutral particle at rest at A decays into two charged particles of different mass Magnetic field is inside the paper Which can be correct paths for two particles if we ignore any gravitational and electrostatic force 19 X X X X X X X X X XX X X XXX X X X X X X X X X XX X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X XXX X collision XXX xDx X X X X XXX X X X X B X X X X X A X X X X X X X X X X X X X X X X XXX X X X X X X X X X X X X X X X X X X X X X XX Y X X X X X X X X X X XX Xx X X X X X X X X XXXXX X XX X X X XX X X X X X X XX XXX X XX X X X X X X X X XXX X X X X XXX X X X X X X X X X X X X XXX XX XXXX XXX XXX X X X X X X XXX XX X X X XXXX X X X X K XXXX XXX X XX X X X X X Xx XX X X X X X X X X X V X X X X XXX X X X X X X X D XAX X X X X X X X 7 X X X XX X 3 XX X X X X XX XDX X X XXX X X X X X X X X X X X X X XXX x X X X X x x X X X X X X X x XX X X X X XX X X X X X X X X X X X X X X X X X Xxx X X X XX X X X XX XX

5 55 Three coaxial circular wire loops and an stationary observer are positioned as shown in figure 5 276 From the observers point of view a current I flows counter clockwise in the middle loop which is moving towards the observer with a velocity v Loops A and B are stationary This same observer would notice that

When a long wire carrying a steady current is bent into a circular coil of one turn the magnetic induction at its centre is B When the same wire carrying the same current is bent to form a circular coil of n turns of a smaller radius the magnetic induction at the centre will be a B n b nB c B n d n B

In the figure ab and cd are two long conduction wires kept parallel to each other at a separation in a uniform time varying magnetic filed The ends a and care connected together by a resistor of resistance R The magnetic induction B perpendicular to the plane of the wires varies with time according to the relation B Bot where B is a positive constant with proper unit and t is the time x Px x in second A conducting wire PQ placed on the wire ab and cd and dragged on the wires with constant speed valong the length of the wires by applying a constant force F Find the value of F in terms of the other given parameters At time t 0 PQ is very close to ac Ignore any resistance electric as well as mechanical other than R B 1 vt 4B 1 vt A B 2B 1 vt R C X a X XP C X X X X D X X D X 8B1 vt X X X X Q X X X X X d X

2 A narrow single slit in air in an opaque screen is illuminated by infrared from a He Ne laser at 1152 2 nm and it is found that the center of the tenth dark band in the Fraunhofer pattern lies at an angle of 6 4 off the central axis a Determine the width of the slit b At what angle will the tenth minimum appear if the entire arrangement is immersed in water nw 1 33

14 A magnetic needle is suspended parallel to a magnetic field The work require to turn it through 1 60 is J The torque require to maintain the 2 needle in this position will be NCERT Pg 158 1 3 Nm 2 2 Nm 3 3 N m

5 4 A flat circular coil of n turns area A and resistance R is placed in a uniform magnetic field B The plane of coil is initially perpendicular to B When the coil is rotated through an angle cf 180 about one of its diameter a charge Q flows through the coil When the same coil after being brought to its initial position is rotated through an angle of 360 about the same axis a charge Q flows through it Then Q Q is A 1 C 1 2 B 2 DO

Determine the current I flowing through a solenoid if the magnetic flux inside its core is found to be 2 60 x 10 4 Wb The radius of the solenoid is 32 0 cm and the number of turns per meter is 235

25 A circular loop of radius R is kept in a uniform magnetic field pointing perpendicular into the plane of paper When a current flows in the loop the tension produced in the loop is Bx x x x x x 1 BIR BIR 2 2 X X X X R Xxx X X X X X X X X I X X X X X X

27 Figure shows the cress sectional view of the hollow cylindrical conductor with inner radius R and outer radius 2R cylinder carrying uniformly distributed current along it s axis The magnetic induction at point P at a distance 3R from 2 the axis of the cylinder will be ff GTE CHIEN Der fra facer staften favel Ryd af 2R fem fa P Zero b 70 i 5 0i 72 R 5oi 2R R 3R 2 f 3 3R12

1 1 rad s 3 1 rad s 15 Consider a uniform square plate mass 1 kg side length 1 m which is tied to a uniform rod of same mass and same length Whole rigid body can rotate in a vertical plane about an axis parallel to the top edge of the plate as shown A particle of mass m 1 kg moving with velocity v collide perpendicularly to the centre of plate If collision is perfectly inelastic and particle sticks to plate after collision then find value of v so that after collision centre of mass of the system just reaches the level of the hinge 3 213g 27 413g 2 rad s 3 4 rad s 4 V 27 2 13g 27 4 16 A uniform circular disc of mass M 1 kg and radius R 1 m is fixed to vertical axis AB with 23g 27 17 18

3 A thin rod of length 2a has a charge of Q uniformly spread along its length a Derive an expression for the electric potential at point A a distance x from the center of the rod b Derive an expression for the electric field at point A X

has he emitted photo te If the work e energy of the 0 Radiations of wavelength 18 x 10 8 metre fall on a metal plate having work function 2eV If a magnetic field of induction 0 5 x 10 4 weber m2 is applied parallel to the plate then calculate the radius of the circular path followed by the photo electrons emitted normally from the plate Ans 0 149 metre in amitted from a FR

4 22 The magnetic field shown in the figure 4 221 consists of two uniform regions The width of the first part is 5cm and the magnetic induction here is 0 001T The width of the other part is also 5cm with the direction of the induction being opposite in direction and 0 002T in magnitude What should be the minimum speed of the electron arriving from the direction indicated in the figure so that it can come out through the magnetic field II in region III Take mass of electron is 9 10 1 kg A x107 m s 9 C 90 16 15x107 107 m s 9 II III No Magnetic field Figure 4 221 4 B x107m m s 9 4 D x 10 m m s