Magnetic Field due to current Questions and Answers

The magnetic induction in air at a distance d from an isolated point pole of strength m unit will be m a b d c m d md d 3 m d

17 You are given many resistances capac inductors These are connected to a variable DC voltage source the first two circuits or an AC voltage source of 50 Hz frequency the next three circuits in different ways as shown in Column II When a current I steady state for DC or rms for AC flows through the circuit the corresponding voltage V and V indicated in circuits are related as shown in Column I Column II P V V HH 3 F Column I A 0 V is proportional to B 1 0 V V C V QV V D 1 0 V is proportional to Codes a A p B q C r D st 9 V V vooooo www 6mH 292 oooooo 6mH S r V V oooooo 6mH t V V 000000 6mH V mos 1kQ 292 V HH 3 F V HH 3 F

is A zero current loop of radius a is placed in a radial field B as shown The net force acting on the loop B 2 Balcos0 1 a 0 C 2 al sine ds D None

ar A solid current carrying conductor of radius R is having current per unit area J as J constant and r is distance from axis Find magnetic field at distance x from axis of wire Assume x R where a is a R 3 Mo ax 3R Mo ax 2 ax 2R 4 Zero

1 Consider a solid sphere of radius r and mass m which has a charge q distributed uniformly over its volume The sphere is rotated about a diameter with an angular speed o Show that the magnetic moment u and the angular momentum 1 of the sphere are related as q 2m 1

30 unite ters a magnetic field B as shown ng with in figure 34 E13 a Find the radius of the circular arc it describes in the magnetic field b Find the angle subtended by the arc at the centre c How long does the particle stay inside the magnetic field d Solve the three parts of the above problem if the charge q on the particle is negative back 39 a mv qB X X X Figure 34 E13 particle of mass m and charge q is projected into a region having a perpendicular magnetic field B Find the angle of deviation figure 34 E14 of the particle as it comes out of the magnetic field if the width d of the region is very slightly smaller than b X mu 2qB d X XB X X X c 71 2mv qB 43

52 An electron is emitted with negligible speed from the negative plate of a parallel plate capacitor charged to a potential difference V The separation between the plates is d and a magnetic field B exists in the space as shown in figure 34 E20 Show that the electron will fail to strike the upper plate if T B mv E ye dm T d d 2m V 2 eBo B 25m qB 93 d c

Two straight long conductors AOB and COD are perpendicular to each other and carry currents and 12 The magnitude of the magnetic induction at a point P at a distance a from the point O in a direction perpendicular to the plane ABCD is 11 12 A C HO 2 a HO 2 1 2 B G D HO 2 11 12 HO 1112 2 1 1

25 Figure 34 E10 shows a circular wire loop of radius a carrying a current i placed in a perpendicular magnetic field B a Consider a small part dl of the wire Find the force on this part of the wire exerted by the magnetic field b Find the force of compression in the wire X X X X Bx X X a X 1 X X X Figure 34 E10 X X

AB lies across the frictionless parallel conducting rails magnitude at t 0 is Bo The rod AB is in a uniform magnetic field B whose given velocity v right ward and it continues to move with same velocity through out the motion The acceleration C Bo B l Bo 8 due to gravity is along negative z axis i e g 10m s k mass of rod following graphs will be the best representation of magnitude of magnetic field versus time A B B D B Bo 8 Bo m Which of the

16 For a ferromagnetic substance the correct graph between X and H is Xm 1 3 Xm R H xm H 2 4 12m H H

I mass m and side r 26 ABC is an equilateral triangular frame It is at rest under the action of horizontal magnetic field B as shown and the gravitational field 0 B T B r 3 3 1 The frame remains at rest if the current in the frame is 2mg rB 2 The frame remains at rest if the current in the frame is 2mg rB 3 71 2 3 The frame is in simple harmonic motion when frame is slightly displaced in its plane perpendicular to AB The r 3 period of oscillation is g 4 For same as in above option the period of oscillation is 71 2 3r 2g

Example 4 13 Evaluate the magnitude and direction of magnetic field at point O in the following cases i a

In vector form Biot Savart s lat Idlx r Ho dB oc 4 K or 3 From Eq i the direction of the cross product vector d 1 the right handed screw rule c Here d B is perpendicular to is directed inwards since p current element Magnetic field induction at entire wire is B Ho 4 Id Ho Id B Ho

Magnetic field at point P due to both infinite long current carrying wires is 2 540 6T 5A 5m 2 5A P 2 5m

Magnetic field strength at the centre of regular pentagon made of a conducting wire of uniform cross section area as shown in figure is 5 i 4 72 2 2 sin B 0 apel C Not zero if current i leaves D point instead of E D Zero even if the current i leaves point D instead of point E a 72 Eyi

Two identical circular loops each of radius r carrying currents i and i are placed co axially at a small distance of separation d Find the force of interaction between them R PK

Two identical small plastic balls are rubbed against a piece of wool such that both of them received approximately 2 10 2 and 2 5 x 10 2 electrons respectively Now both the charged balls are kept at a distance of 25 cm in air Calculate the nature and magnitude of force between both the balls

xample 4 12 a A current carrying circular loop lies on a smooth horizontal plane Can a uniform magnetic field be set up in such a manner that the loop turns around itself i e turns about the vertical axis b A current carrying circular loop is located in a uniform external magnetic field If the loop is free to turn what is its orientation of stable equilibrium Show that in this orientation the flux of the total field external field field produced by the loop is maximum c Aloop of irregular shape carrying current is located in an external magnetic field If the wire is flexible why does it change to a circular shape

c Must every magnetic configuration have a north pole and a south pole What about the field due to a toroid d Two identical looking iron bars A and B are given one of which is definitely known to be magnetised We do not know which one How would one ascertain whether or not both are magnetised If only one is magnetised how does one ascertain which one Use nothing else but the bars A and B

olenginio D The magnetic field at all points inside the pipe is the same but not zero Figure shows cross section view of a infinite cylindrical wire with a cylinderical cavity current density is uniform J jok as shown in figure Of notl A Field inside cavity is uniform B Field inside cavity is along a Only Inpirov enam C Field inside cavity is perpendicular to a ning oldst Istuoshod a no iqail ofbeen moo A qnd won ai zasqmoo bas noit od 11 Istroshod wolad 00 jedroxized of olyns fedy D If an electron is projected with velocity vo j it will move undeviated before colliding with cavity wall

Figure shows a long straight wire of a circular cross section radius a carrying steady current I The current is uniformly distributed across this cross section Calculate the magnetic field in the region r a and r a P

25 An equilateral triangle of side length 1 is formed from a piece of wire of uniform resistance The current I is fed as shown in the figure Then the magnitude of the magnetic field at its centre O is b a 3 l 2 l c Hol 2 l C 3 3 l b 2 l d zero

5 At a point on the right bisector of a magnetic dipole the magnetic a potential varies as 1 b potential is zero at all points on the right bisector c field varies as r d field is perpendicular to the axis of dipole

points A and Cof a circular conductor ABCD with O as centre and angle AOC 60 If B and B are the magnitude of the magnetic fields at O due to the B B currents in ABC and ADC respectively then ratio is 1 1 3 5 AF IAA B O 60 D C 1272 4 6 16 P X

A horizontal metallic rod of mass m and length is supported by two vertical identical springs of spring constant K each and natural length fo A current i is flowing in the rod in the direction shown If the rod is in equilibrium then the length of each spring in this state is A fo i B mg K B lo i B mg 2K C lo mg i B 2K D lo mg i B K OB

61 A solenoid has length 60 x 10 2 m and its total number of turns is 2400 An iron rod is placed inside it along its axis The relative permeability of iron is 1500 If the current in the solenoid be 0 6 A find the magnetic field B and magnetic intensity H inside the rod Calculate the intensity of magnetisation of the Ans 4 52 T 2400 Am 36 x 106 Am rod A

A current carrying circular loop of radius R is placed in the xy plane with centre at the origin Half of the loop with x 0 is now bent so that it now lies in the yz plane Then NCERT Exempla a The magnitude of magnetic moment now diminishes b The magnetic moment does not change c The magnitude of B at 0 0 z z R increases d The magnitude of B at 0 0 z z R is unchanged

If a current is passed through a circular loop of radius R then magnetic flux through a coplanar square loop of side as shown in the figure l R is 1 3 Mol R 2 l Mol R 26 R l 2 4 Mole 2R MoTR 1

Example 4 8 Figure 4 15 shows a long straight wire of a circular cross section radius a carrying steady current I The current I is uniformly distributed across this cross section Calculate the magnetic field in the region r a and r a

The bob of a simple pendulum is replaced by a magnet The oscillation are set along the length of the magnet A copper coil is added so that one pole of the magnet passes in and out of the coil The coil is shortcircuited Then which of the following happens 1 period does not change 2 oscillations are damped 3 amplitude increases 4 period decreases ason

a 4 b 3 c 2 d 2 Consider a long straight wire of cross sectional area A carrying a current i Let there be n free electrons per unit volume An observer places himself on a trolley moving in the direction opposite to the current with a speed u and separated from the wire by a distance r The magnetic field seen by the observer is very nearly t nAe Ho i Ho i 2 i b zero 2 r Tr Tr a c d

A current carrying wire AB with current i is placed as shown in figure Find the magnetic field at origin 6 YA 1 0 01 Molo T 3 0 49 olo TU 0 3 io B 4 0 2 4 0 15 olo TU Holo TC

Two long conductors are arranged as shown above to form overlapping cylinders each of radius r whose centers are separated by a distance d Current of density J flows into the plane of the page along the shaded part of one conductor and an equal current flows out of the plane of the page along the shaded portion of the other as shown What are the magnitude and direction of the magnetic field at point A blow norusis HeimVacuum Conductor L el inlog omsa od nave A 2 dJ in the y direction B H 2r d r in the y direction D 2 Jr d in the y direction

path XY as shown The abcd is a coil adjacent to the path of electron What will be the direction of current if any induced in the coil X b a C electron d Y Re AIPMT 2015 1 No current induced 2 abcd 3 adcb 4 The current will reverse its direction as the electron goes past the coil Dolhi 110005 Ph 011 47623456

A disc of radius r and carrying positive charge q is rotating with an angular speed o in a uniform magnetic field B about a fixed axis as shown in figure such that angle made by axis of disc with magnetic field is 0 Torque applied by axis on the disc is A C qor Bsin 0 2 qor Bsin 0 clockwise Disc Fixed axis dio u B anticlockwise D B qor Bsin 0 482 qor Bsin 0 A 3 anticlockwise clockwise bhulungna sil to

27 shows a rod PQ of length 20 0 cm and mass 200 g suspended through a fixed point O by two threads of lengths 20 0 cm each A magnetic field of strength 0 500 T exists in the vicinity of the wire PQ as shown in the figure The wires connecting PQ with the battery are loose and exert no force on PQ a Find the tension in the threads when the switch S is open b A current of 2 0 A is established when the switch S is closed Find the tension in the threads now PA S

Example 11 11 When light of wavelength 4000 A is incident on a barium emitter emitted photoelectrons in a transverse magnetic field strength B 52x10 6 T moves in a circular path Find the radius of the circle Given work function of 31 kg barium is 2 5 eV and mass of electron is 9 1 x107 e 1 6x10 1 C h 6 6x10 34 Js

8 Two identical long conducting wires AOB and COD are placed at right angle to each other such that one is above the other and O is their common point The wires carry and 1 currents respectively Point P is lying at distance d from O along a direction perpendicular to the plane containing the wires The magnetic field at the point P will be CBSE AIPMT 2014 Ho 4 a Ho 2nd c H0 1 12 2nd b Ho d Inti 1 1 2nd Ho 1 12 1 2nd

The value of magnetic field at O is 1 2 1 Zero Hol 2 2a 3 1 Hoi 4 none of these a a 0 vi 2

A thin cir ying direction is lying in the x y plane with its centre at the origin A uniform magnetic field of strength B B 27 31 sk tesla is applied in the region The ring can rotate about the axis AA only and AA is in x y plane neglect effect of gravity B B A C Bolo rads m 5ml B 2 The magnitude of initial angular acceleration of the ring is A 2B 1 r 31 21 rads2 B D zero P m O 450 AL rads2

2 A wire is bent in the form of an equilateral triangle of side 100cm and carries a current of 2A It is placed in a magnetic field of induction 2 0T directed perpendicular into the plane of paper The direction and magnitude of magnetic force acting on each side of the triangle will be X X X X X X X x B X X 1 2 N normal to the side towards centre of the triangle 2 2 N normal to the side away from the centre of the triangle 3 4 N normal to the side towards centre of the triangle 4 4 N normal to the side away from the centre of the triangle

3 An a particle is moving with the velocity v ul u in a uniform magnetic field B Bk Magnetic force on a particle is 2 euB i j 4 2euB i j 1 2euB i j euB 1 1 3

B 1 v vo 2 v v 3 v v 4 v v The armature coil of dynamo is rotating The generated induced emf varies and the number of magnetic lines of force also varies Which of the following condition is correct 1 lines of flux will be minimum but induced emf will be zero 2 lines of flux will be maximum but the induced emf will be zero 3 lines of flux will be maximum but induced em will be not be zero 4 the lines of flux will be maximum and the induced emf will be also maximum

A charged particle of mass m and charge q travels on a circular path of radius r in a uniform perpendicular magneti field B The time taken by the particle to complete half revolution is 2 m qB m qB q mB 2 q mB

West A proton of mass m and charge q enters a magnetic field B with a velocity v at an angle with the direction of B radius of curvature the resulting path is MIV qB sin 0 qB B my qB sin 4 mv cos qB

Proton Deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field The radii of proton deuteron and alpha particle are respectively rr and r Which one of the following relation AIEEE 2012 is correct 4 r r r 1 r r r C P 2 r r r 0 P 3 r r r

2 rd nd 1 mv m V 3 m m and v V 700 Two particles A and B of masses m and m respectively and having the same charge are moving in a plane A magnetic field exists perpendicular to this plane The speeds of the particles are v and v respectively and the trajectories are as shown in the figure Then X MALA mv m Va 4 m m and v VB

In a coaxial straight cable the central conductor and the outer conductor carry equal currents in opposite directions The magnetic field is zero outside the cable 3 inside the outer conductor 2 inside the inner conductor 4 in between the two conductors

1 expand 2 compress Wires 1 and 2 carrying currents i and i respectively are inclined at an angle 0 to each other What is the force on a small element dl of wire 2 at distance r from wire 1 as shown in figure due to the magnetic field of wire 1 AIEEE 2002 1 i i dl tan 0 Ho 2fr Ho 3 4T i i dl cos 0 1 dl 2 4 Ho 2fr i i dl sin 0 Ho 4fr i i dl sin 0 doflected in a magnetic field The compound can emit E 20021