Magnetic Field due to current Questions and Answers

A magnet is kept fixed with its length parallel to the magnetic meridian An identical magnet is parallel to this such that its center lies on perpendicular bisector of both If the second magnet is free to move it will have 1 translatory motion only 2 rotational motion only 3 both translatory and rotational motion 4 vibrational motion only

carrying current has the shape as shown in adjoining figure Linear parts of the wire are very long and parallel to X axis while semicircular portion of radius R is lying in Y Z plane Magnetic field at point O is AIPMT 2015 1 B 2k R 2 B 1 Ho X 5 r 2k 4t R Z 3 B H 1 Ho Ho ri 2k 4t R Y

magnetic field of 3 57 x 10 2 T If the value of elm is 1 76 x 10 1 C kg the frequency of revolution of the electron is NEET Phase 2 2016 1 1 GHz 2 100 MHz 3 62 8 MHz A

A short magnet of moment 6 75 A m produces neutral points on its axis If the horizontal component of earth s magnetic field 5 x 10 5 Wb m then the distance of the neutral points from the centre of magnet 1 10 cm 2 20 cm 4 40 cm 3 30 cm

1 10 cm 2 20 cm A straight wire carries current in vertical upward direction A point P lies just east of it at a small distance and another point Q lies to the west just same distance The magnetic field at these points consider earth magnetic field 1 B Bo 2 Bp Bo 3 B B 4 None 51

A particle with a specific charges s is fired with a speed v towards a wall at a distance d perpendicular to the wall What minimum magnetic field must exist in this region for the particle doesn t hit the wall 1 2 3 V sd V 2v sd V

2 A piece of wire carrying a current of 6 00 A is bent i the form of a circular arc of radius 10 0 cm and subtends an angle of 120 at the centre Find th magnetic field B due to this piece of wire at the centre

A particle of charge per unit massa is released from origin with a velocity voi in a uniform magnetic field B Bok If the particle passes through 0 y 0 then y is equal to 1 2V0 Boa 2 Vo Ba 2V0 3 Boa A particle with a specific charges s is fired with a speed v towards a wall at a distance d perpendicular to 4 Vo Boa According to Biot length dl and inve containing dl and dBx LL Idlxr r

Current in the coil I 18 A The magnitude of the magnetic field a B H 21 B 10 x 2x16x RX 20 0 16 O is towards right i e East according to right hand The direction of magnetic field due to the coil x at centre thumb rule The magnitude of the magnetic field at the centre of coil y O expres clockwise the centre of coil x Mathematically 4RX10 T 21 10 x 2xx 18 x 25 0 1 4 Ty 1 2 9 x 10 T towards left i e West according to right hand thumb The direction of magnetic field due to coil y at centre O is rule Here the magnitude of B is greater than B so the resultant magnetic field will be in the direction of B i e left West 1 C 1 AMPERE S CIRCUITAL LAW According to this law the line integral of a magnetic field B around any closed path in vacuum is o times the net current Inet enclosed by the curve Boundary 1 2 TOPIC 2 Ampere s Circuital Law and Moving Surface 36 9 5f Bet Resultant is given tan d current Am always facil applied in field of a st discussed B d1 Honet Ampere s law is applicable only for an Amperian loop as the Gauss s law is used for Gaussian surface in electrostatics The choice of an Amperian loop has to be such that at each point of the loop either 1 B is tangential to the loop and is a non zero constant ii B is normal to the loop iii B vanishes Ampere s circuital law has same content as the Biot Savart s law Both of these relate magnetic field and current and Magn Straig Magneti distance taken as Ang Hen

its applications and at last the chapter will are discussed in detail so it will be more interesting to understand and torque between two parallel conductors All the topics carefully after going through each and every sentence very t thoroughly TOPIC 1 Magnetic Field and Its Applications MAGNETIC FIELD magnetic field Similarly a moving charge or current flowing through a conductor produces a In electrostatics we studied that a static charge produces an electric field in the surroundings of a magnet or a current carrying conductor in The SI unit of magnetic field is tesla T or weber metre 2 Wbm or which its magnetic influence can be experienced is called magnetic field The space NAm and its CGS unit is 1 gauss G 1 tesla 104 gauss Oersted s Experiment

4 A singly ionized q e organic molecules with mass Mo 115 u is accelerated through an electrostatic potential V and enters the region with uniform magnetic field B directed out of the page with speed Vo 1856 m s it hits a strip at the distance Do 6 4 cm Another singly ionized q e organic molecule with mass M 132 u is accelerated through the same potential V and is deflected in the same magnetic field B a What is the speed of the organic molecule with mass M as it enters the region with magnetic field O V O Do O

166 An electron is moving in a field of induction 21 2j T with a velocity of 5 x 10 J ms The force acting on the electron is 1 1 6 x10 N 3 6 10 N 2 3 2 10 N 4 15 2 10 10N

Two identical particles having the same mass m and charges q and q separated by a distance d enter in a uniform magnetic field B directed perpendicular to paper inwards with speeds v and v2 as shown in figure The particles will not collide if K X X X X m a d v V Bq X 2m c d v V X V2 X X X X x B d 12 X X m V V Bq b d

D 90 In the figure shown there are two semicircles of redii r and r in which a current I is flowing The magnetic induction at the centre O will be A 5 5 Hi 4 C H 11 12 4 4742 B D Hoi Moi 1 12 4 rr

Illustration 6 a particle is moving along x axis in x y plane with velocity of 10 m s A magnetic field of magnitude is present in the region along Z axis Find out the direction and magnitude of force on the particle 2x16x10 C 3 2x10 C

3 Two long straight wires are placed along x axis and y axis They carry current and 12 respectively The equation of locus of zero magnetic induction in the magnetic field produced by them is 1 y x x X 3 y x 1 3 X 2 y 4 y 1 x

3 AD BP C F The magnetic field of earth at the equator is approximately 4x10 T The radius of earth is 6 4x100 m Then the dipole moment of the earth will be nearly of the order of 2014 1 1023 A m 3 10 6 A m 2 1020 A m 4 10 0 A m

to the current 1 5 m below the Two identical conducting wires AOB and COD are placed at right angles to each other The wire AOB carries an electric current I and COD carries a current I The magnetic field on a point lying at a distance d from O in a direction perpendicular to the plane of the wires AOB and COD will be given by A Mo 1 7 1 2nd Ho C 1 1 2nd B D 1 Ho 1 2nd d Ho 2nd 1 1 1 2

4r Two circular coils X and Y have equal number of turn and carry equal currents in the same sense and subtend same solid angle at point O If the smaller coil X is midway between O and Y then if we represent the magnetic induction due to bigger coil Y at O as By and that due to smaller coil X at O as Bx then X9 Y 1 W By 1 Bx 3 By Bx 1 2 X 4 V 40 2 4 By Bx By Bx 2 x 4

Hysteresis loops for two magnetic materials A and B are given below B B F H H A B These materials are used to make magnets for electric generators transformer core and electromagnet core Then it is proper to use 2016 1 A for electromagnets and B for electric generators 2 A for transformers and B for electric generators 3 B for electromagnets and transformers 4 A for electric generators and transformers

A coil of wire having inductance and resistance has a conducting ring placed coaxially within it The coil is connected to a battery at time t 0 so that a time dependent current 1 t start flowing through the coil If l2 t is the current induced in the ring and B t is the magnetic field at the axis of coil due to 1 t then as a function of time t 0 the product 12 t B t I 1 6th A increases with time B decreases with time C does not vary with time D passes through a maximum 2000

Two identical wires A and B each of length e carry the same current I Wire A is bent into a circle of radius R and wire B is bent to form a square of side a If BA and BB are the values of BA is 2016 BB magnetic field at the centres of the circle and square respectively then the ratio 1 3 7 16 2 77 8 2 2 4 TT 16 8

A magnetic needle of magnetic moment 6 7 x 10 Am and moment of inertia 7 5 10 6 kg m is performing simple harmonic oscillations in a magnetic field of 0 01 T Time taken for 10 complete oscillations is 2016 1 8 76 s 3 8 89 s 2 6 65 s 4 6 98 s

3 urrent i is moving in a hexagon shaped loop of side length a Find expression for magnetic field at centre hexagon 1 2 Hoi 1 a 4 3 oi a 3

The vertical component of earth s magnetic field at a place is 75 of the horizontal component The value of angle of dip at that place is NCERT Pg 187 1 53 3 45 2 37 4 60

A particle of mass m and charge q moving with velocity qBl in the figure Region Il has a uniform magnetic field B perpendicular to the plane of paper The particle will enters region Il normal to the boundary as shown 2m Region l 1 Enter the region III 3 Complete circular motion in region II sh Educatio Region II x X x x x Region III 2 Not enter the region III 4 Move undeflected in region II

11 Find 8 di over following loops direction in which integration has to be performed is indicated by arrows 101 0 II Oi 12 iv 1 O

used needle a point O The arrow shows the direction of its magnetic moment The other arrows show different positions and orientations of the magnetic moment of another identical magnetised needle Q a In which configuration the system is not in equilibrium b In which configuration is the system in i stable and ii unstable equilibrium c Which configuration corresponds to the lowest potential energy among all the configurations shown 94 95 to otp 92 93

2 Two point charges qA 3 Cand qB 3 C are located 20 cm apart in vacuum a What is the electric field at the midpoint O of the line AB joining the two charges b What is the force experienced by a negative test charge of magnitude 1 5 10 C placed at this point

3 A wire of length 1 carrying a current I along the Y direction is kept in a magnetic field given by B j k T The magnitude of B Lorentz force acting on the wire is a Bn c BI b BIL d Bl BIL

A straight current carrying wire is placed along the axis of a current carrying loop then force between them is 1 Repulsive 3 Zero 2 Attractive 4 Cannot be prediotod

continues to move undeviated then the strength of the magnetic field induciton B is 14 tesla A beam 30 mev ox particle is to be obtained from a 50 cm cyclotron The strength of magnetic field required to be applied will be in T A clycotron is used to obtain 2 Mev protons if the frquency is 5MHz and the potential is 20 kv

16 Magnetic field at point O due to the given structure is 1 3 Mo 4 R 2 Mol 2 R 1 1 R R 2 O 2 4 1 1 60 Hol T 4 R 2 Hol O 2 R 1 och Educational Services Limited Regd Office Aakash Tower 8 Pusa Road New Delhi

A very long solenoid is made out of a wire with n turns per unit length The radius of the cylinder is a and is negligible compared to its length 1 The interior of the cylinder is filled with materials such that the linear magnetic permeability varies with the distance r from axis according to r H constant for 0 r b H constant for b r a The self inductance of the solenoid is a n b b b a c 1 b a b d n b a

Draw the pattern of lines of force due to a magnetic field through and around a current carrying loop of wire How does the strength of magnetic field produced at the centre of the loop be affected if a strength of the current passing through it is doubled b the radius of the loop is reduced to half the original value c the radius of the loop is doubled its original value and at the same time current passing through it is also doubled

a closed loop with a smaller are of radius R and a bigger arc of radius 2R placed in a radial magnetic field the center of the loop coincides with the center of the field and its strength varies as B kr then the magnetic force on the loop will be r is the distance of the point from the center C 1 31kR 5 131KTR R 2R 1908 2 B 21kmR 3 7IkR

Four infinitely long L shaped wires each carrying a current i have been arranged as shown in the figure Obtain the magnetic field intensity at the point O equidistant from all the four corners

6 A copper disc of radius 0 1 m is rotated about its centre with 20 revolutions per second in a uniform magne field of 0 1 T with its plane perpendicular the field The emf induced across the radius of disc is TL 1 20 3 2 mV volt 2 4 20 millivolt 20 V

A charged particle enters a magnetic field at right angles to the magnetic field The field exists for a leny equal to 1 5 times the radius of circular path of the particle The particle will be deviated from its path by 1 90 3 30 2 sin 180 2 3 T SAVART LAW 2 y

What current would be maintained in a circular coil of wire of 1000 turns and 10 cm in radius in order to just cancel the earth s magnetic field at a place where the horizontal component of Earth s magnetic field is 2 10 T Ans 0 4A

As shown in diagram a current carrying conductor is subjected to steady uniform magnetic field Then on conductor 1 Torque t 0 force F 0 2 Torque t 0 force F 0 3 Torque t 0 force F 0 4 Torque T 0 force F 0 B

5 Given figure shows a coil with a edges of length 1 m and carrying a current of 1A There exists in space a uniform magnetic field of 2T in positive y direction Find the torque on the loop ZA

An element Al Axi is placed at the origin and car ries a large current I 10 A Fig What is the mag netic field on the y axis at a distance of 0 5 m Ax 1 cm PO 0 5m

Bnet 2B 4 CA ixal xb 216 Z y T M x B Masino 2ilb 81 Ty 2ilbB A uniform magnetic field given by Bj is applied in the region the net torque experienced by the loop is 1 ilbB 3 ilhB 2 2ilB 4 Zero 3 RC 1 3 In ex If is

15 Find the magnetic field at the centre P of square of side a shown in figure 2 2 1 i

15 Two straight long conductors AOB and COD are perpendicular to each other and carry currents i and i2 The magnitude of the magnetic induction at a point P at a distance d from the point o in a direction perpendicular to the plane ABCD is C A 1 H0 1 1 2nd 101 10 1 2 2 1 2 D Bi 791 Bi 2 B Mo 1 12 4nd Mo 111 iz

given diagram substance A Zn and substance B Mn are placed at the ends of a long current carrying solenoid then Solenoid A C B Mi Zv 1 A will move away from the center C and B will move towards the center C 2 A will move towards C and B will move away the center C 3 Both will move away from the center C 4 Both will move towards the center C

A circular coil of radius R is carrying current 1 The ratio of magnetic fields at the centre of the coil and at a point at a distance 8 R from the centre of the coil on the axis of the coil is

4 1 2 FIN 5 A hollow sphere of mass m radius R is rotating about its diameter with angular velocity s If charge Q is uniformly distributed over the surface ther magnetic moment of sphere is NCERT Pg 182 3 2 Nm QR 3 QR 5 QR

A circular coil of radius R 10 cm having 500 turns and total resistance 2 92 is placed initially perpendicular to the earth s magnetic field of 3 x 10 5 T The coil is rotated about its vertical diameter by an angle 2 in 0 5 seconds The induced current in the coil is a 0 5 mA 1 5 mA b 1 0 mA d 3 0 mA