Magnetic Field due to current Questions and Answers

The current density j inside a long solid cylindrical wire of radius R 12 mm is in the direction of the central axis and its magnitude varies linearly with radial distance r from Jor R the axis according to J where J 10 A m Find the magnitude of magnetic field at r 6mm in uT

13 Find the total energy stored in the capacitors given in the circuit Fig 5 N 4 Delhi 2004 Ans 3 6 x 10 5 X and Y 6V C 1 F Golf CAF C4 2 F 1 F Etter C3 Fig 5 N 4 2 F C5 2 F

carrying square loop is placed near an infinitely long current carrying wire as shown in the figure The torque acting on the loop is D P 2T 12 i i r 6 hizr 2T 2 Zero 1 i ilog 2 r Fract Answer

no Hare Ma 1 nuol sin TC n COS I fed TC n I 2 COS tan n Ans 1 1 2 4 3 1 4 3 5 3 6 3 es TU 3 nu I TC sin tan T 4 22 4 nuol yoy The Magnitude of the Magnetic field at the centre the equilateral arm of in side in which the current of C flowing will Bo

Magnetic Effect of Current 1 fed face fay face and land find the Magnetic field intensity at the went o for 1 a Ans H01 1 1 00 a Hol MERSER g b G b Hol 1 1 a given current 8 distribution

5 You are given an isolated capacitor of capacitance C without dielectric charged to a potential difference V How many times will each of the following become if a dielectric slab of dielectric constant 4 is inserted between the plates completely filling the space between the plates a capacitance c field between the plates b potential difference d energy stored by the capacitor Ans a 4 b c d 1 A

A uniform magnetic field exists in a circular region of radius r The magnitude of magnetic field is B and point inwards An electron flies into the region radially as shown in figure after a certain time the electron gets deflected by the magnetic field and leaves the region The time interval during which the electron move in Nmtan 1 eBr mV the region is Then find value eB of N m is mass of electron and e is charge of electron XXXX Xx

5 Two identical circular loops P and Q each of radius r and carrying equal currents are kept in the parallel planes having a common axis passing through O The direction of current in P is clockwise and in Q is anti clockwise as seen from O which is equidistant from the loops P and Q Find the magnitude of the net magnetic field at O 2r I D P 6 II Delhi 2012

1 Het and O ions mass of Het 4 amu and that of 02 16 amu they pass a region of constant perpendicular magnetic field If kinetic energy of all the ions is same then 1 Het ions will be deflected more than those of 02 2 He ions will be deflected less than those of O2 3 All the ions will be deflected equally 4 No ions will be deflected

A long cylinderical wire of radius b carries a current i distributed uniformly over its cross section Find the magnitude of the magetic field at a point inside the wire at a distance a from the axis

0 Equal currents are flowing in three infinitely long wires along positive x y and z directions The magnetic field at a point 0 0 a would be i current in each wire 1 2 2na 2 4 M D 2 a 2ma i j

In a square loop PQRS made with a wire of cross section current I entres from point P and leaves from point S The magnitude of magnetic field induction at the centre O of the square is a R 1402 21 4T 2 O 0 4 21 4 a O Ho Ho 2 21 4 a O Zero P S H Marks 4 1

A conductor has three segments two straights of length L and a semi circular with radius R It carries a current I What is the magnetic field B at point P A C H I 4 R HI 4R I L R II P B D 2 I L III Ho I 4T R H I 4t

0 B 0 b E 0 B 0 c E 0 B U If a projected charge passes through a zero gravity region remains undeviated or undeflected then fin possible cases of electric field and magnetic field in that region a E 0 B 0 b E 0 B 0 c E 0 B 0 d E 0 B 0 ito coad may be constant then find possi

A short bar magnet placed on the table along the north south line Its north pole is directed towards geographic north then location of neutral points is A North B South C East 1 A and B 2 C and D 3 A and D D West 4 B and C

A magnetic field is applied at perpendicular to the axis of cylinderical discharge tube then cathode and positive rays deflected in 2 Opposite direction 4 No deflection for both 1 Same direction 3 Mutually perpendicular direction 1 Cathode rays Positive rays Anode Cathode Discharge tube

2 The momentum Na 3 The kinetic energy 4 None of these 22 A long straight hollow conductor tube carrying a current 22 ure has two sections A and C of unequal cross sections joined by a conical section B 1 2 and 3 are points on a line parallel to the axis of the conductor The magnetic fields at 1 2 and 3 have magnitudes B B and B respectively then 163 d B A 1 B B B 2 B B B 3 B B B 4 B cannot be found unless the dimensions of the section Bare known Two iss 1 p2mic 2B ALLE 3 4 T and the B LB A Y R f 1 2 a 3 af 1 2 B B A B Mod 40 d 1 B B B 2 B B B3 3 B B B 4 i den for Ban app Ac 25

QA particle of mass m and charge q is released from the origin in a region occupied by electric field E and magnetic field B such that B Boj E If the subsequent equation of motion of the particle in z direction is given by z a R 1 coswt Find a

A particle of mass m and charge q is moving ir region where uniform constant electric and m fields E and B are present E and B are parallel other At time t 0 the velocity Vo of the partic perpendicular to Assume that its speed is a c the speed of light in vacuum If the velocity particle at time tis qB

If a projected charge passes through a zero gravity region without change in its velocity then find por cases of electric and magnetic field in that region a E 0 B 0 b E 0 B 0 c E 0 B 0 d E 0 B 0 undeflected the

75 In a coil current falls from 5 A to 0 A in 0 2 s If an average emf of 150 V is induced then the self inductance of the coil is a c 4 H 3 H b d 2 H 6 H

electromagnetic wave is given by cos kz wt E Eo 2 At t 0 a positively charged particle is at the point x y z 0 0 7 If its instantaneous velocity at t 0 is vok the force acting on it due to the wave is

0 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 east then direction of magnetic field is 1 Towards east 2 Vertically downwards 3 Towards west 4 Vertically upwards f E

In a certain region uniform electric field Ek and magnetic field B B are present At time t 0 a particle of mass m and charge q is given a velocity v voj vok Find the minimum speed of the particle and the time when it happens so Bo Eo

1 In the figure galvanometer G gives maximum deflection when lllllll ele S N a magnet is pushed into the coil b magnet is rotated into the coil c magnet is stationary at the centre of the coil 6 ma way ma a c Far

c ac is induced in the loop d no current is induced in the loop In the given figure current from A to B in the straight wire is decreasing The direction of induced current in the loop is a clockwise c changing O b anticlockwise d nothing can be said 35 dire a c 36 A AB

2 The figure shows a wire sliding on two parallel conducting rails placed at a separation 1 A magnetic field B exists in a direction perpendicular to the plane of the rails The force required to keep the wire moving at a constant velocity v will be a evB b HoBv 4xl XXXX X xx xx xx x X X X X X X X c Blv d zero

A hollow cylinderical wire carries a current I having inner and outer radii R and 2R respectively Magnetic field at a point which 3R 2 distance away from its axis is 1 5 ol 18TR 2 Hol 36 R 3 5 ol 36 R 4 5 ol 9 R

d The end A of the solenoid potential uires 33 An infinitely long cylinder is kept parallel to a uniform magnetic field B directed along positive z axis The direction of induced current on the surface of cylinder as seen from the z axis will be a clockwise of the positive z axis anticlockwise of the positive z axis b c zero d along the magnetic field uniform magnetic d 39 A 160 betw 20 a m a c 40 A

2 The north pole of a long bar magnet was pushed slowly into a short solenoid connected to a galvanometer The magnet was held stationary for a few seconds with the north pole in the middle of the solenoid and then withdrawn rapidly The maximum deflection of the galvanometer was observed when the magnet was a moving towards the solenoid b moving into the solenoid c at rest inside the solenoid d moving out of the solenoid

10 A current carrying long wire is placed along the z axis The current is flowing along the ve z direction Find the B due to this wire at i d 0 0 1 ii 0 d 0 y X iii 0 0 d iv d d 0

of earth s a 3 9 x 107 tesla c 8 0 x 10 tesla b 3 9 x 10 tesla d 7 0 x 107 tesla 3 A long straight horizontal cable carries a current of 2 5 A in the direction 10 south of west to 10 north of east The magnetic meridian of the place happens to be 10 west of the geographic meridian The earth s magnetic field at the location is 0 33 G and the angle of dip is zero Locate the line of neutral points ignore the thickness of the cable At neutral points magnetic field due to a current carrying cable is equal and opposite to the horizontal component of earth s magnetic field a 15 15 mm c 35 15 mm b 30 15 mm d 40 15 mm

66 A ring of mean radius 15 cm has 3500 turns of wire wound on a ferromagnetic core of relative permeability 800 The magnetic field in the core for a magnetising current of 1 2 A is a 2 48 T b 3 48 T d 5 48 T c 4 48 T 67 A solenoid has a core of a material with relative

Kh 3H For the tangent galvanometer when tana a is the angle of the compass with respect to the earth magnetic field Be S N versus the current in the coil I in mA is plotted as shown in the figure What is the magnitude of the horizontal magnetic field of the earth Be in micro Tesla The number of turns of the coil is N 500 the diameter is 15 cm Select one a 33 b 66 C 53 d 15 O O lang 5 5 0 781 21 2 747 1 mA

63 A domain in ferromagnetic iron in the form of cube is having 5 x 100 atoms If the side length of this domain is 1 5 um and each atom has a dipole moment of 8 x 1024 A m then magnetisation of domain is a 11 8 x 10 Am c 11 8 x 10 Am b 1 18 x 10 A m d 1 18 x 10 Am

c 3 93 Nm A dipole of magnetic moment m 30j A m is placed along the y axis in a uniform magnetic field B 21 5 T The torque acting on it is a 40 kN m b 50 kNm c 60 kN m d 70 kN m 10 T

110 36 A magnetic dipole is under the influence of two magnetic fields The angle between the field directions is 60 and one of the fields has a magnitude of 1 2 x 102T If the dipole comes to stable equilibrium at an angle of 30 with this field then the magnitude of the field is a 1 2 10 T c 1 2 10 T b 2 4 x 10 T d 2 4 x 10 T

c 3 5 Nm 29 The torque required to hold a small circular col of 10 turns area 1 mm and carrying a curren 21 of A in the middle of a long solenoid o 10 turns m carrying a current of 2 5 A with its ax perpendicular to the axis of the solenoid is Solenoid Axis 0 Coil a 1 5x 10 Nm c 1 5 x 10 N m 84 b 1 5x 10 Nm d 1 5 x 10 N m

B A circular coil of magnetic moment 0 355 IT te with its plane normal to an external field of magnitude 5 0 x 10 T The coil is free to turn about an axis in its plane perpendicular to the field direction Whe the coil is turned slightly and released it oscille about its stable equilibrium with a frequency of 2 The moment of inertia of the coil about its axis of rotation is a 1 13 x 10 kg m b 1 13 x 10 kg m c 1 13 x 10 kg m d 1 13 x 10 kg m wire is placed wa 24 25

9 A long straight hollow conductor tube carrying a current has two sections A and C of unequal cross section joined by a conical section B 1 2 and 3 are the points on a line parallel to the axis of the conductor The magnetic fields at 1 2 and 3 have magnitude B B and B 3 B A C D 1 B B B 1 2 3 2 B B B

2 The magnitude of the equatorial magnetic field due to a bar magnet of length 2 cm at a distance of 1 m from its mid point is magnetic moment of the bar magnet is 0 60 A m a 5 0 10 T c 7 0 10 T b 6 0 10 d 8 0 10 T T

Two identical bar magnets are fixed with their centres at a distance d apart A stationary charge is placed at P in between the gap of the two magnets at a distance D from the centre O as shown in the figure The force on the charge Qis S N a zero b directed along OP c directed along PO d directed perpendicular to the plane of paper 27 28

3 What is the magnitude of axial field due to a bar magnet of length 3 cm at a distance of 75 cm from its mid point if its magnetic moment is 0 6 A m b 0 113 T d 0 313 T a 0 013 T c 0 213 T 20

A conducting ring of circular cross section with inner and outer radii a and b is made out of a material of resistivity p The thickness of the ring is h It is placed coaxially in a vertical cylindrical region of a magnetic field B krt where k is a positive constant r is the distance from the axis and t is the time If the current kh ap through the ring is I b a then what is the value of a B B h

Two students are investigating electromagnets and collect the data found in the table below in a classroom experiment Magnetic field strength T 250 500 755 1 250 2 505 of turns in wire coil 10 20 30 50 100 Which of the following conclusions is supported by the data the students collected A Doubling the turns of wire in an electromagnet will triple its strength OB Doubling the turns of wire in an electromagnet will double its strength OC Doubling the electric current in an electromagnet will double its strength OD Doubling the electric current in an electromagnet will triple its strength

A solenoid has a core of material with relative permeability 200 The windings of the solenoid are insulated from the core and carry a current of 4 A If the number of turns is 500 per metre then the magnetic intensity H is 1 A m 2 10 A m 0 5 A m 0 1 A m

7 A circular coil of 70 turns and radius 5 cm carrying a current of 8 A is suspended vertically in a uniform horizontal magnetic field of magnitude 1 5 T The field lines make an angle of 30 with the normal of the coil then the magnitude of the counter torque that must be applied to prevent the coil from turning is a 33 Nm b 3 3 Nm c 3 3 x 10 2 N m d 3 3 x 10 Nm

5 In a moving coil galvanometer the deflection 0 the scale by a pointer attached to the spring is N a NA kB b KAB NAB c d NAB kl

P and Q are two long wires which carry 4 A current each along the positive z direction out of the page in the figure P is located at x 3 m and Q at x 3 m What is the x component of the force on a 5 m segment of the wire Q due to the magnetic field produced by the wire P y P 3 m O A 2 67 x 106 N 3 m X

A proton of mass m charge q enters a magnetic field B with a velocity v at an angle 0 with the direction of B The radius of the resulting path is Vino my 20 1 mv qB 2 mv sine qB