Magnetic Field due to current Questions and Answers

OF A wire of length e carries a current bent into various regular polygons shown below Find magnetic moment in terms of length of the wire a Equilateral triangle b Square c Regular hexagon d Circular loop 0 P ka

A bar magnet of magnetic moment M is cuts into two equal parts in following two fashions a Paralle to its length b Perpendicular to its length then what happens to the magnetic moment of each part

Two long wires carrying same currents are placed perpendicular to each other The magnetic force on a small length dL of second wire is 1 Hol dL 2 L M 2 dL 2 L 3 H dL Mol 2 Mol 4 L dL L

The rectangular wire frame as shown in figure has a width d mass m resistance R and a large length A uniform magnetic field B exists to the left of the frame A constant force F starts pushing the frame into the magnetic field at t 0 a Find the acceleration of the frame when its speed has increased to v b Show that after some time the frame will move with a constant velocity till the whole frame enters into the magnetic field Find this velocity v c Show that the velocity at time t is given by v v 1 et v Xxx X X X X X X X

49 A wire carrying a current i is placed in a magnetic field in the form of the curve y a sin iBL Force acting on the wire is 1 n 2 iBL 3 2iBL X TX X X X xOx 0 x 2L X X X K X X X X X X X X X X X X 2L X

A rectangular coil of length 0 12 m and width 0 1 m having 50 turns of wire is suspended vertically in a uniform magnetic field of strength 0 2 Weber m The coil carries a current of 2 A 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 Re AIPMT 2015 1 0 12 Nm 2 0 15 Nm

28 Magnitude of magnetic field at a point P due to a current carrying wire starting from origin and extended along y axis is Y 1 3 4 3 i O P 3 4 m 2 X 3 i 16 Moi

Paragraph for Q Nos 12 and 13 An infinitely large conducting slab of thickness t is centered at y 0 in X Z plane as shown in figure The surface current density in the slab is uniform Ja k Answer the following questions 12 Magnetic field above the slab y A Hot 7 A 13 Plot graph between magnetic field with y axis 18 C 1 02 72 1 2 is Sve y 1 2 B i D AB 1 2 H 1 2 0 2 1 2

Two short bar magnet of length 1 cm each have magnetic moments 1 20 Am and 1 00 Am respectively They are placed on a horizontal table parallel to each other with their N poles pointing towards the South They have a common magnetic equator and are separated by a distance of 20 0cm The value of the resultant horizontal magnetic induction at the mid point O of the line joining their centres is close to Horizontal component of earth s magnetic induction is 3 6x10 5Wb m JEE Main 2013 a 3 6x10 5Wb m 350x104Wh m b 2 56 10 Wb m d 5 80x104Wh m

6 1 A uniform magnetic field of intensity B sin 2t directed into the plane of the paper exists in the cylindrical region of radius 1 m A uniform loop of resistance 100 folded in the form of equilateral triangle of side length 2m is placed as shown in figure Find the maximum potential drop in volt in wire AB A x x 1m X x 30 x B

Q 5 A rectangular loop of wire lies on the xy plane where there is a magnetic field B B2 The total length of the wire is L but its side lengths are variable Consider a situation where the side lengths of the rectangular loop area and A current I flows in the loop Consider the configuration where the torque on the loop is maximised with the loop always being on the xy plane Then what is the magnitude of the magnetic dipole moment of the loop Max score 1 Neg score 0 IL IL 16 2 IL 32 X

Q 2 Particle A of mass M and charge Qis travelling in circular motion on the x y plane where a uniform magnetic field B Bk exists The radius of its circular path is RA In the same magnetic field particle B has mass 4M and charge Q and has twice the kinetic energy of A The radius of the circular path for B is RB What RB is the value of RA Max score 1 Neg score 0 2 2 2 4 2

40 3 infinitely long parallel wires carry currents as shown The force experienced by wire C per unit length is A B C E Ho 612 2n d 2 31 Ho 2 d 21 P 3 d Ho 2nd 31 4 0

A long straight wire of a circular cross section of radius R carrying steady current i The current is uniformly distributed across the cross section The graph corresponding to the magnetic induction B w respect is the normal distance r from the centre of the wire is like B B 1 R R r 2 1 B R R

A solenoid 4 cm in diameter and 20 CM in length has 250 turns and carries a current of 15 ampere calculate the flux through the surface of a disc of 10cm radius that is positioned perpendicular to and centred on the axis of the solenoid

In given figure X and Yare two long straight parallel conductors each carrying a current of 2 A The force on each conductor is F When the current in each is changed to 1 A and reversed in direction the force on each is now F 4 F 2 X 2 A 4 2 A and unchanged in direction and reversed in direction and unchanged in direction 2 and reversed in direction

A pair of parallel horizontal conducting rails of negligible resistance shorted at one end is fixed on a table The distance between the rails is L A conducting massless rod of resistance R can slide on the rails frictionlessly The rod is tied to a massless string which passes over pulley fixed to the edge of the table

Statement 1 The magnetic field due to finite length of a straight current carrying wire is symmetric about the wire Statement 2 Ampere law can be used to find magnetic field due to finite length of a straight current carrying wire 1 Statement 1 is true statement 2 is true and statement 2 is correct explanation for statement 1 2 Statement 1 is true statement 2 is true and statement 2 is NOT the correct explanation for statement 1 3 Statement 1 is true statement 2 is false 4 Statement 1 is false statement 2 is true

Equal antiparallel currents are directed in two parallel wires so that one is out of the page and the other is into the page as shown Compare the magnitude of the magnetic field B at any arbitrary point equidistant from the wires to the magnitude of the field B at that point from one wire alone X 1 B B for all equidistant points 2 B B for all equidistant points 3 B B for closer equidistant points only 4 B B for closer equidistant points only

An infinitely long wire lying along z axis cames a current 1 flowing towards positive z direction There is no other current consider a circle in x y plane with centre at 2 meter 0 0 and radius 1 meter Divide the circle in small segments and let de denote the length of a small segment in anticlockwise direction as shown Pol Im 2 2 0 0 Rd7 Consider two points A 3 0 0 and B 2 1 0 on the given circle The path integral B de of the total magnetic field g along the perimeter of the given circle from A to B is 78 x

13 A hypothetical magnetic field existing in a region is given by B B e where e 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 the X Y plane and the centre at 0 0 d Find the magnitude of the magnetic force acting on the loop

Question 1 A uniform magnetic field B exists in circular region of radius R as shown which is decreasing with time at a constant rate There is a concentric wooden rings which have uniformly distributed charge Q and radius 2R and another concentric copper ring of radius 3R then select incorrect statement Assume rings are placed on frictionless surface 3R R 2R Options a There will be induced current in the copper ring b Induced electric field at 2R is more in magnitude than at 3R c Induced electric field at 2R is less in magnitude than at 3R d Wooden ring will rotate

Which of the following statement is correct MP PET 2008 a Electric field is zero on the surface of current carrying wire b Electric field is non zero on the axis of hollow current carrying wire c Surface integral of magnetic field for any closed surface is equal to o times of total algebraic sum of current which are crossing through the closed surface 1 None

Two identical current carrying coaxial loops carry current I in an opposite sense A simple amperian loop passes through both of them once Calling the loop as C Question Type Single Correct Type 1 B de ol 2 0 of B de the value of of sense of C is independent 3 at all the points on C B and de are perpendicular

3 20 4 25 15 Same current is flowing in three infinitely long wire along positive x y and z directions The magneti at a point 0 0 a would be 1 3 Hol 2 Hol i 1 2 2 Hol 2 4 16 Magnetic field at point O due to the given structure is i 1 Mol k 2

Question 11 Inside a homogenous long straight fixed cylindrical wire of circular cross sectional area a cylindrical cavity is made whose axis is parallel to the conductor axis and displaced relative to it by a distance R 2 A direct current of density j flows along the wire whose top view and side view are shown in the figure A point positive charge q and a negat vi respectively at point C charged particle q of equal mass m are with velocity 8my R Given that and all collisions are perfectly elastic Proton 8 m b 9 JR Smooth 16 c MJR and Axis of conductors The time period motion of negative charged particle is given by Options 4 a 9 JR

d KE PE 4 In the figure shown the four rods have resistance per unit length The arrangement is kept in a magnetic field of constant magnitude B and directed perpendicular to the plane of the figure and directed inwards Initially the sides as 07 b 0 c tan d ultr from 8 The ele with x shown form a square Now each wire starts mo constant velocity v towards opposite wire At an neglect the interaction between the wires a induced emf in the circuit is 4 Bv 0 2v b induced current in the circuit with direction c force required on each wire to keep its velocity B v a po X b for 9 wi c the to d a A rec conta its bo the b

3 Figure shows a conducting disc rotating about its axis in a perpendicular uniform and constant magnetic field B A resistor of resistance R is connected between the centre and the rim The radius of the disc is 5 0 cm angular speed 40 rad s B 0 1 T and R 1 2 The current through the resistor in milliampere is

22 Two metal strips each of length 1 are clamped parallel to each other on a horizontal floor with a separation b between them A wire of mass m lies on them perpendicularly as shown in figure 34 E8 A vertically upward magnetic field of strength B exists in the space The metal strips are smooth but the coefficient of friction between the wire and the floor is u A current i is established when the switch S is closed at the instant t 0 Discuss the motion of the wire after the switch is closed How far away from the strips will the wire reach 201 S T 1

1 In all other cases A wire of uniform resistance per unit length is bent to form an equilateral triangle of side L A current I flows into one corner and flows out of an adjacent corner as shown The magnetic field at the centroid of triangle due to the current in the triangular frame is A 3 gl 2TTL

at 2 kg ice at 20 C is mixed with 5 kg water 20 C Then final amount of water in the mixture would be Given specific heat of ice 0 5 cal g C Specific heat of water 1 cal g C Latent heat of fusion for ice 80 cal g 1 6 kg 2 5 kg 3 4 kg x 4 2 kg

A long straight wire carrying current I is moving with speed v toward a small circular coil of radius r containing N turns which is attached to a voltmeter as shown The long wire is in the plane of the coil Only a small portion of the wire is shown in the diagram V Part 1 The radius of the coil is 0 02 m and the coil has 11 turns At a particular instant I 4 amperes v 3 7 meters per second and the distance from the wire to the center of the coil x 0 16 m B dt a What is the magnitude of the rate of change of the magnetic field inside the coil You will need to calculate this algebraically before you can get a number Write an expression for the magnetic field due to the wire at the location of the coil Use the dx approximate formula since the wire is very long Remember the chain rule and remember that v dt Save for Later Part 2 i N turns radius r i Voltmeter Save for Later b What is the magnitude of the voltmeter reading Remember that this includes all 11 turns of the coil volts T s Attempts 0 of 3 used Attempts 0 of 3 used Submit Answer Submit Answer

3 Electron 4 Alpha particle 20 A proton is moving towards north along horizontal line passes through a zero gravity region where electric and magnetic field are mutually perpendicular to each other The path of particle remains undeviated or undeflected If the direction of electric field is towards cast then direction of magnetic field is 1 Towards east 2 Vertically downwards 4 Vertically upwards 3 Towards west ngy axis then directi

A current carrying closed loop in the form of a right angle isosceles triangle ABC is placed in a uniform magnetic field acting along AB If the magnetic force on the arm BC is F the force on the arm AC is 1 A 2F B Question Type Single Correct Type C

46 Two equal electric currents are flowing perpendicular to each other as shown in the figure Lines AB and CD are perpendicular to each other and symmetrically placed with respect to the currents Where do we expect the resultant magnetic field to be zero 1 On CD D On AR

State the following statements are true or false a The magnetic field inside straight solenoid of finite length is always less than onl b The magnetic field of an infinitely long ideal solenoid of radius R carrying current I is constant ins and zero outside M S 2

4 38 A current carrying conductor is placed as shown in figure The magnitude of magnetic field at point P will be 1 3 Ho 2i T 4 r 2 3 5 Ho RIN T 4nr 2 2 r P Ho 2 1 1 1 Mo 2i 4 r 2 Mo i T 4 140 1 1 4 r

1 An experimenter s diary reads as follows a charged of particle is projected in a magnetic field 7 07 30 x 10 T The acceleration of the particle is 3 found to be 7 05x10 6 ms 2 The number to the left of i in the last expression was not readable What can this number be

A ring of mass m and radius R is set into pure rolling on horizontal rough surface in a uniform magnetic field of strength B as shown in the figure A point charge q of negligible mass is attached to rolling ring Friction is sufficient so that it does not slip at any point of its motion is measured in clockwise from po de mmmmmm Ring will continue to move with constant velocity The value of friction acting on ring is Bqv cos The value of friction acting on ring is Bqv sin mg 9 P

Consider a set of six infinitely long straight parallel wires arranged perpendicular to the plane of paper at vertices of a hexagon an carrying currents as shown in the figure The length of the each side of the hexagon is 3 cm What is the magnitude and direction of the magnetic field at point P 3 A 2 A 3 A 1 20 uT 2 A P 3 A 2 40 UT up 47 La 3 A 1

A solid cylindrical wire of radius R carries a current 1 The magnetic field is 5 mu T at a point which is 2R distance away from the axis of wire Magnetic field at a point which R 3 distance inside from the surface of the wire is 10 3 mu T 20 3mu T 5 3 mu T 1012 T

Two thick wires and two thin wires all of the same materials and same length form a square in the three different ways P Q and R as shown in figure with current connection shown The magnetic field at the centre of the square is non zero in cases P 1 in Q only 3 in Q and R only R 2 in P and Q only 4 P and R only

A metallic ring is attached with the wall of a room When the north pole of a magnet is brought near it the induced current in the ring will be a first clockwise then anticlockwise b in clockwise direction c in anticlockwise direction d first anticlockwise then clockwise S N a

There is a small metallic ring of radius lo and having negligible resistance placed perpendicular to a constant magnetic field Bo One end of a rod is hinged at the centre of ring O and other end is placed on the ring Now rod is rotated with constant angular velocity mo by some external agent and circuit is connected as shown in the figure initially switch is open and capacitor is uncharged If switch S is closed at t 0 then calculate heat loss from the resistor R2 from t 0 to the instant when voltage across the capacitor becomes Vo Assume plane of ring to be horizontal and friction to be an absent at all the contacts Assume R 2R Bolo 4V 2 1 2 A CV2 Lcv 6 C CV B Bo O xx XX S R www www R

A long straight wire of circular cross section of radius 5 cm is carrying a steady current of 10 A uniformly distributed over its cross section If the magnetic field induction at 2cm from the axis of the wire is same as that at a distance x from its surface then x is A 15cm B 7 5cm C 25cm D 15cm

A cylindrical conductor of radius R carries a current i nonuniformly spread over its cross section The current density J Jo 2 3r R where r is the radial distance and Jo is constant Then B at r 4R is Select one O a Jo R 2 mio O b Jo 2R mio O c Zero O d JoR 2n mio O e Jo 2R mio

15 A conducting rod AB moves parallel to x axis in a uniform magnetic field pointing in the positive direction The end A of the rod gets Y D B 1 positively charged 3 neutral X 2 negatively charged 4 first positively charged and then negatively charged

3 A thin convex lens made from crown glass has focal length f When it is measured in two different liquids 4 5 having refractive indices and it has the focal lengths f and f respectively The correct relation between the focal lengths is a f f f

A beam of electrons passes undeflected through mutually perpendicular electric and magnetic fields If the electric field is switched off and the same magnetic field is maintained the electrons move 1 along a straight line 2 in an elliptical orbit 3 in a circular orbit 4 along a parabolic path

To a circular wire two straight wires are attached as shown When current is passed through it the magnetic field at the centre is zero Hoi 4R B B 0 B B Hoi AR 3 i 2 1 2