Magnetic Field Questions and Answers

Q1 Show that the magnetic field induction at any arbitrary point due to a short bar magnet is B 3cos 0 1 Hence using this equation Hom 4 r show that magnetic field at a point on the axis is Baxis symbols carry their usual meaning Ho 2m 4n 3 Where 5 marks

7 A uniform conducting wire ABC has a mass of 10 g A current of 2 A flows through it The wire is kept in a uniform magnetic field B 2 T The acceleration of the wire will be B X X 4 cm X X X x A x X 1 Zero 2 12 ms 2 3 1 2 10 ms 4 0 6 10 3 ms X 5 cm X X X X C

A coil of 1000 turns is wound on a book and this book is lying on the table The vertical component of earth s magnetic field is 0 6x 10 T and the area of the coil is 0 05 m The book is turned over once about a horizontal axis in 0 1 s This average emf induced in the coil is 0 03 V 0 06 V zero 0 6 V SOLUTION 30 2 lel 4 Ar 2NBA 2 1000x0 6 10 0 05 At 0 1

A conducting rod PQ of length 5 m oriented as shown in figure is moving with velocity 2m s i without rotation in a uniform magnetic field 4k Tesla Emf induced in the rod is in volts YI 5m 53 2m s X

The magnetic field in the plane electromagnetic wave is given by B 2 x 10 7 sin 0 5 x 103 x 1 5x 10 1 t tesla The expression for electric field will be Question Type Single Correct Type 1 E 2 30 sin 0 5 x 10 x 1 5 1011 t V m 2 E 60 sin 0 5 x 10 x 1 5 x 1011 t V m 3 Ey 30 V 2 sin 0 5 x 101 1x 0 5 x 10 t V m 4 Ey 60 sin 0 5 x 10 x 1 5 x 1011 t V m

The angle of dip at a place on the earth gives Question Type Single Correct Type 1 The horizontal component of the earth s magnetic field 2 The location of the geographic meridian 3 The vertical component of the earth s field

Q 4 A square wire loop of side 2a lies on the xy plane with its centre at the origin The wire loop carries current I in the clockwise direction There is a magnetic field B ky along the z direction where k is a constant What is the magnitude of the net force on the wire loop due to the current Max score 1 Neg score 0 O kla 2

Q 3 A uniform magnetic field B Bk exists only on the upper half of the x y plane i e for x 0 Particle A of charge Q 0 and mass M enters the field at the origin moving along the positive direction of the y axis It exits from the region that contains the magnetic field in time TA Particle B of the same charge Q and mass 2M enters the field at the origin again moving along the positive direction of the y axis B exits from the region that contains the magnetic field in time TB What is the magnitude of TB TA Max score 1 Neg score 0 TM QB TM 2QB 2TM QB 2T M

3 A current element of length 1 mm carrying 10 A is place along y axis at the origin The magnetic fi induction produced by it at 1m Om is 1 10 T 2 10 K T 3 2 10 T 4 2x10 1 T A proton moving with constant velocity passes through

4 5 A proton moving with constant velocity passes through a region of space without change in its velocity It E and B denotes electric and magnetic fields respectively the region of space may have 1 E 0 B 0 2 E 0 B 0 3 E 0 B 0 4 All of these Two concentric Co planar circular coils of radius 1 m and 2 m carry currents 104 and 200 racpoctiv

38 A toroid with inner radius 4 m and outer radius 6m contains 10 turns and carrying 100A current magnitude of magnetic induction in its interior is 1 4 mT 2 6 mT 3 9 mT 4 12 mT

5 5 Two concentric Co planar circular coils of radius 1 m and 2 m carry currents 10A and 20A respective in opposite direction The value of magnetic induction at the centre is 1 4 10 T 2 2 x10 T 3 TX10 T 4 OT OB de over the loop is

7 Consider the two idealised systems i a parallel plate capacitor with large plates with small separation and ii a long solenoid of length L R radius of cross section In i E is ideally treated as a constant between plates and zero outside In ii magnetic field is constant inside the solenoid and zero outside These idealised assumptions however contradict fundamental laws as below NCERT Exemplar a Case i contradicts Gauss s law for electrostatic fields b Case ii contradicts Gauss s law for magnetic fields c Case i agrees with E dl 0 d Case ii contradicts Hd1 I em

Two identical short bar magnets are placed at 120 as shown in the figure The magnetic moment of each magnet is M Then the magnetic field at the point P on the angle bisector is given by P 1 Mo M 4 d N Mo 2 2M AT 13 d S120 S 2 N Mo 2M 4 d 4 Zem

15 Two current carrying conductor are placed on smooth surface as shown in figure then for conductor CD where a and a are acceleration and angular acceleration respectively B A 1 a 0 0 3 a 0 0 C D 2 a 0 0 4 a 0 0

A charged particle enters a uniform magnetic field with a certain speed at right angles to it In the magnetic field a change could occur in its J K CET 2006 MP PMT 2013 a Kinetic energy b Angular momentum d Speed c Linear momentum

21 40 A and B are two concentric circular conductors of centre O and carrying currents and 2 as shown in the adjacent figure If ratio of their radii is 1 2 and ratio of the flux densities at O due to A and B is 1 3 then the value of 1 12 is B 1 1 4 1 1 2 14

The magnetic needle of a tangent galvanometer is deflected by an angle 60 due to a magnetic field of the current carrying coil at the centre of the coil The horizontal component of earth s magnetic field 0 34 x 10 4 T The magnetic field of coil is 1 96 x 10 4 T 5 9 x 10 4 T 5 9 10 5 T 5 9 x 105 T

1 At the instant A very long straight wire carries when a charge Q at point P has velocity V as shown CBSE PMT 2005 the force on the charge is a Opposite to OX c Opposite to OY P V b Along OX d Along OY

SolveLancer Test Which of the following statement is are correct 1 Flemings left hand rule is used to determine the direction of current Induced in conductor moving in magnetic field II Force due to magnetic field is always perpendicular to direction of motion of charged particle III Like electric field magnetic field also forms a closed loop IV Left hand thumb rule gives direction of magnetic field around a current carrying wire SolveLancer Test a I II III IV b III IV c II III d II

35 The wire loop carries a current I as shown in the figure The magnetic field at the centre O will be 1 Hol 2 2 4 17 1 1 2 Po 4 Zero

A current carrying string in shape in ring of radius 1m is placed in uniform magnetic field perpendicular to plane of ring The current and area of cross section of ring are 1 amp and 0 2cm The density of string is 2 10 kg m The speed of wave in the string ring is 10 m sec Find magnetic field in T Neglect any other interaction BO i 1A

20 pts 6 A radioactive source emits beta particles electrons mass 9 11 x 10 31 kg with energy 1 x 106 eV 1 6 10 13 J The electrons enter a uniform magnetic field as shown If the electrons emerge from the left side of the field at a right angle to their initial direction what are the minimum strength and direction of the field B 1 cm

For static electric and magnetic fields in an inhomogeneous source free medium which of the following represents the correct form of two of Maxwell s equations 1 V 0 V B 0 2 0 B 0 3 V 0 V B 0 X 4 V XE 0 V B 0

tration 1 A rectangular loop of area 0 06 m is placed in a magnetic field 1 2 T with its plane inclined 30 to the field direction Find the flux linked with plane of loop

The next two questions pertain to the situation described below Two fixed conductors are connected by a resistor R 16 Q The two fixed conductors are separated by L 1 7 m and lie horizontally A conducting bar of mass m 0 4 kg slides on them at a constant speed v producing a current of 0 65 amps A magnetic field shown by the black dots in the figure with magnitude 2 4 T points out of the page 10 How fast is the bar moving 6 pts v 4 33 m s v 8 67 m s v 7 37 m s v 2 55 m s Ov 0 159 m s 11 What is the magnitude of the magnetic force on the bar moving at this speed 3 pts F 1 02 N F 2 65 N 05 0 16 N R 6 pts 3 pts

33 A 800 turn coil of effective area 0 05 m is kept perpendicular to a magnetic field of 5 x 10 5 T When the plane of the coil is rotated by 90 around any of its coplanar axis in 0 1 s the emf induced in the coil will be a 2 V b 0 2 V c 2 x 10 V d 0 02 V 34 In which of the following devices the eddy current effect

Question Try Yourself 19 Wha t is net magnetic field at point 0 R 1 ii 2r ut i 0 i 2r R O ey RO sy r vi Try Yourself 19 What is net magnetic field at point O i 2r ii hmmp NY Fancle R O 2r

Two infinitely long wires are placed perpendicular to the plane of paper Current in wire A is 8 in outward the plane of paper and current in B is io inward the plane of paper The a SB de along the QP is kupio Find the value of k O Pi a 8 B 8

A V COO urged particles am eving directly above de moing horizontady out of the BO D who cane care conductor at the instant show above The signe of the charges and directions for the che is moving y upeat particle Cis mening t and particir moving horontaly is the right Four charged particles are moving directly above or below a horizontal current carrying conductor at the instant shown above The signs of the charges and direction of motion of the charges are indicated in the figure Particle A is moving horizontally out of the page particle B is moving vertically upward particle C is moving horizontally into the page and particle D is moving horizontally to the right Which two charged particles will not experience a magnetic force at this instant Select two answers

Figure shows four Gaussion surfaces consisting of identical cylindrical midsections but different end caps The surfaces central axis of each Cylindrical midsection the end caps have these shapes S convex hemispheres S concave hermisphere S3 cones S4e flat disks rank the surfaces acccording to a the net electric flux through them and b the electric flux through the top end caps greatest first S S S S

ALLE The magnetic field at the centre of a current carrying ring is Bo and at a small axial distance x R R radius of the ring is B Then B Bo Bo 2 5 3 3 2 2 4 None of these 23

A straight current carrying conductor is kept alon the axis of circular loop carrying current The forc exerted by the straight conductor on the loop i A Perpendicular to the plane of the loop B In the plane of the loop away from the cente C In the plane of the loop towards the cente D Zer

1 ng a current is Pa a uniform magnetic field If the magnetic fo segments PS SR and RQ are F F respectively and are in the plane of the pa along the directions shown the force segment QP is P F S 1 F3 F F 2 F3 F F F 2 F3 R AIPMT Prelims

Question 4 Numeric Type A square loop ABCD of side length a and mass m of each side is kept in a uniform magnetic field region B B as shown in the figure The loop is constrained to rotate only about the y axis It rotates only due to the torque of the magnetic force acting on it Calculate its angular speed in rad s when it has rotated through an angle 90 Initially the loop was lying in the x y plane The loop is carrying current I as shown in figure Given 3IB m

A length of wire carries a steady current It is bent first to form a circular coil of one turn The same length is now bent more sharply to give a double loop of smaller radius The magnetic field at the centre caused by the same current is Select an answer A B C D a quarter of its first value unaltered four times of its first value half of its first value

A parallel plate capacitor consists of square plates of edge a separated by a distance d that is much smaller that the edge length It is charged to a potential V and made to move with a constant velocity directed along one of its edges How much magnetic field exists inside the capacitor A V d B VV 0 0 a C vod v a D None of these

A circular loop carrying a current I is placed in the xy plane as shown in figure An uniform magnetic field B is oriented along the positive z axis The loop tends to I y B Question Type Single Correct Type

Figure shows infinitely long bent wires in the plane of paper and each carrying a current i with O as origin and x and y axis as shown co ordinates of points P Q are 2m 0 and 6m 0 respectively Magnetic induction at P is given by Hoi Fill the value of a in OMR sheet 32T Y 90 90

44 41 A positively charged particle moving due Ea enters a region of uniform magnetic field directed vertically upwards This particle will 1 Move in a circular path with a decreased speec 2 Move in a circular path with a uniform speed 3 Get deflected in vertically upward direction onos

A closed surface with dimensions a b 0 40 m and c 0 60 m is located as in the figure below The left edge of the closed surface is located at position x a The electric field in the region is non uniform and is given by E 3 0 47x i N C where x is in meters Calculate the net electric flux leaving the closed surface 2 y x a 1 X

swer you will be awarded 4 Marks and for WRONG answer there is a negative marking of 1 Mark N A long current carrying wire is bent in the following shape What is the magnetic field at it s centre O 1 3 oi 8r 3 Ho 4x r 37 2 0 U 3 oi 8r 4

5 A loop ABCDEFA of straight edges has six corner points A 0 0 0 B 5 0 0 C 5 5 0 D 0 5 0 E 0 5 5 and F 0 0 5 The magnetic field in this region is B 31 4k T The quantity of flux through the loop ABCDEFA in Wb is

A conductor ABCDEF moves along its bisector with a velocity of 1 m s through a perpendicular magnetic field of 1 Wb m as shown in fig If all the five sides are of 1 m length each then the induced emf between points A and F is AX 1 0 TAN 71 V B 60 x x Ex F 2 IV 4 3 V

independent magnetic field is pulled out with constant velocity v as shown in the figure om http cbseportal com om http cbseportal com X X X X X X X X X X X X X X X X X X X X X a X X X X X X X X X X X X X X X X X X vx X X Page 7 Court

A charged particle with charge q enters a region of constant uniform and mutually perpendicular fields E and B with a velocity v perpendicular to both E and B and comes out without any change in magnitude or direction of v Then 1 v Ex B B 2 v Bx E B 3 V ExB E 4 v Bx E E

negatively charged particle p is placed initially at rest in a constant uniform gravitational field and a constant uniform electric field as shown in the diagram What qualitatively is the shape of the trajectory of the electron 1 2 3 OP DU

Which of these pairs of devices operate in reverse of each other a generator and a motor b generator and electromagnet Oc electromagnet and resistor d motor and electromagnet

22 In an a c series circuit the instantaneous current is maximum when the instantaneous voltage is maxi mum The circuit element connected to the source will be b pure capacitor a pure inductor c pure resistor d combination of a capacitor and an inductor

Three coaxial circular wire loops and an stationary observer are positioned as shown in figure 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 The same observer would notice that 000 B 1 Clockwise currents are induced in loops A and B 2 Counter clockwise currents are induced in loops A and B 3 A clockwise current is induced in loop A but a counter clockwise current is induced in loop B 4 A counter clockwise current is induced in loop A