Magnetic Field due to current Questions and Answers

Two charge particle are projected as in figure The minimum value of d for which they do not collide X X X X 3 X X q m d X x 1 d m v Bq X v V X X 2m X V V d X X 4 X m 2 d v V Bq q m d 2m V V

A dip circle is oriented with its plane at an angle of 30 with the magnetic meridian at a place The apparent angle of dip shown by the dip circle is 45 The true angle of dip at the place will be tan tan 2 tan 4 2 tan 11

4 Two wires A and B are having lengths of 40 cm and 30 cm respectively Both of them are bent in the form of a circle such that current i is passed through A and in through B To have the same magnetic induction at the centre the ratio of i i is 1 2 3 2 3 2 3 3 4 4 4 3

A magnet of magnetic moment Moscillating freely in earth horizontal magnetic field makes n oscillations per minute It the magnetic moment is doubled and the earth s horizontal field is also doubled then number of oscillations made per minute would be O 2n n 4 2n 2 2n

bead as a function of time is aq Rt 1 2Bo at 2 aq Rt m 4m Ho1 1 1 47b 2 Hol 121 27b Figure shows a long straight current carrying wire with a current I and a thin s width b and length 1 placed parallel to it with a current 12 as shown in figure Fi magnetic force of interaction between current 11 and 12 r b 1 In b In 3 H0 1 21 In 37b as here a is a positive constant The contact force between the ring and Y r b b singo 1 b 2Bo at aq Rt 4m Bdue to infinite long straight wire is inward Boix2 F Force on strip dife to Wire dire 4TX dF 12Bd sine FM122 dFl 1 8d2 Moll 1 r b In zb b 2112 Bo at Moil 275 4aq Ri m 4 129 4 x Two circular loops are parallel coaxial and almost in contact 1 00 mm apa

A charged particle q m enters perpendicularly in a uniform magnetic field B and comes out of field as shown The angle of deviation 0 and time taken by particle to cross magnetic field will be 1 sin 2 sin Bqd me my Bq Bqv me md Bq 3 cos 1 Bqd me Ra x q m x X X X M X

A circular loop of radius r carrying a current i is held at the centre of another circular loop of radius R r carrying a current I The plane of the smaller loop makes an angle of 30 with that of the larger loop If the smaller loop is held fixed in this position by applying a single force at a point on its periphery what would be the minimum magnitude of this force

3 Current in primary coil of a mutual inductor is 2 A and is increasing at the rate of 3 A s If mutual is 4 H find flux and emf in secondary coil 1 12 Wb 8 V 3 12 Wb 6 V 2 6 Wb 12 V 4 8 Wb 12 V

14b A small loop of area 8 mm is placed inside a long solenoid that has 854 turns em and carries a sinusoidally varying current I of amplitude 1 28 Amp and angular frequency 230 rad s The central axes of the loop and solenoid coincide What is the amplitude of the emf induced in the loop

4 13 Two circular coils X and Y having equal number of turns 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 the bigger coil Y at O as B and that due to smaller coil x at O as B x then A C B V B B B 2r Y 0 25 1 X Figure 4 206 B D B B B y B X d 2 0 5 2

4 31 Determine the magnetic field at point P located a distan x from the corner of an infinitely long wire beant at right angle as shown in figure 4 257 The wire carries a steady current i P i

A magnet of magnetic moment M oscillating freely in earth s horizontal magnetic field makes n oscillations per minute If the magnetic moment is doubled and the earth s horizontal field is also doubled then number of oscillations made per minute would be 2n n 2

um force s motion the form a and b ough the A charged particle of mass m and charge q enters along AB at point A in a uniform magnetic field a existing in a rectangular region of size axb The particle leaves the region exactly at the comer point C Find the speed of particle Dr X 3 100 B qB a 6 2mb qB a b 2ma X X M C X H X H 2 qB a b 2mb Two long conductors separated by a distance qB a b 2ma 4 d

Q25 A 1 0 m long wire carrying a steady current of 1 56 A is lying along the x axis as shown in Figure 10 The wire has a mass of 100 g and is placed in a uniform magnetic field If the current is in the positive x direction find the magnetic field in tesla that will keep the wire suspended in the air L A 0 628 k B 0 716 C 0 531 1 D 0 560 k E 0 719 j

ths 1 A current carrying wire is placed in the grooves of an insulating semicircular disc of radius Ras shown The current enters at A and leaves at B Determine the magnetic field at D 1 3 1 Hol 8 R 3 3 Hard 30 13 0 B OFRO Hol 2 4R 3 4 None of these 31 3 F

2iB A conducting ring of mass 2kg and radius 0 5ms placed on a smooth horizontal plane The ring carries a current of 4A A horizontal magnetic field of 10T is switched on at t 0 The initial angular acceleration of ring will be O 100 M 1 40m rad s 2 20m rad s 3 5m rad s 4 15m rad s 5 A long vertical wire in which a current is flowing

17 The magnetic induction at the centre O Fig is 3 3 l I 8a 8b 8 2 3 1 HI 8a 8b 3 l l 8a 8b 17 3 Hol 2a 2b 3 l 8a l 8b 2 4 3 I HI 8a 8b 3 l l 8a 8b

Question No The path of a charged particle entering in a uniform magnetic field making an angle 60 with the field is O Circular O Straight O Elliptical Helical

A magnetic field is produced and directed along y axis A magnet is placed along x axis The direction of torque on the magnet will be O In the x y plane O Along y axis Along z axis Torque will be zero

A non conducting thin spherical shell of radius R has uniform surface charge density o The shell rotates about a diameter with constant angular velocity w Calculate magnetic induction B at the centre of the shell 2 HowR P owR 2 34R

2 50 A regular hexagonal loop of side a is formed b uniform wire A current flows into it as shown magnetic field at the center C of the hexagon is 1 Moi 16 3 gi C Moi 2 24 4 Zero

242 5 A disc of radius R rotates with constant angular velocity about its own axis Surface charge density of this disc varies as o ar where r is the distance from the centre of disc Determine the magnetic field intensity at the centre of disc a awR Ac HoawR 8 b HoawR 6 d HoawR 3 6 A partiele of mass mand having a positive charge q is projected from origin with speedy along x axis in a 10 A charge mass space c electric field E particu E a B M A wi

A battery is connected between two points A and B the circumference of a uniform conducting ring of radius r and resistance R One o the arcs AB of the ring subtends an angle at the centre The value of the magnetic induction at the centre due to the current in the ring is a zero only if 0 180 c proportional to 2 180 0 b zero for all values of e d inversely proportional to r 4 B

Figure 35 E9 shows a part of an electric circuit Th wires AB CD and EF are long and have identica resistances The separation between the neighbourin wires is 10 cm The wires AE and BF have negligib resistance and the ammeter reads 30 A Calculate th magnetic force per unit length of AB and CD

A square loop PQRS carrying a current of 60 A is placed near a long wire carrying 10 A as shown in figure 35 E10 a Show that the magnetic force acting on the part PQ is equal and opposite to that on the part RS b Find the magnetic force on the square loop 2cm R OP

hiform wire of mass 10 kg cm is held at rest in a horizontal position without any support by placing it in a uniform perpendicular magnetic field The wire is carrying current of 10A The magnetic field is Take g 10ms 0 T IT 10 T

4 52 A closely wound coil has a radius of 6 00cm and carries a current of 2 50A How many turns must it have if at a point on the coil axis 6 00 cm from the centre of the coil the magnetic field is 6 39 104T Ans 69

Nonuniform displacement current density The figure shows a circular region of radius R 3 00 cm in which a displacement current is directed out of the page The magnitude of the density of this displacement current is Ja 4 00 A m 1 r R where r is the radial distance r R What is the magnitude of the magnetic field due to the displacement current at a r 2 00 cm and b r 5 00 cm

20 The horizontal component of the earth s magnetic field at a given place is 0 46 and the angle of dip 1s 30 Calculate the value of i vertical component and ii total intensity c earth s magnetic field

Consider a wire frame shown in figure The wire frame is made by joining two equilateral triangle of side length 1 m It is placed in uniform magnetic field 8 4 T acting perpendicular to the plane of frame If it is given that current in each branch of the frame is 2 A then the magnitude of magnetic force acting on the frame is N 8 Answer To B 8 C T F F E E

Two concentric circular loops of radii r and 12 carry clockwise and anticlockwise currents i and i If the centre is a null point i i must be equal to 2 2 1 r r 2 r r 3 r r 4 r r 2

1 A straight wire of length 0 5 metre and carrying a current of 1 2 ampere is placed in a uniform magnetic field of induction 2 tesla If the magnetic field is perpendicular to the length of the wire the force acting on the wire is 1 24N 3 3 0 N 2 1 2 N 4 2 0 N

A coil of single turn is wound on a sphere of radius R 1 m and mass m 2 kg The plane of the coil is parallel to the plane and lies in the equatorial plane of the sphere Current in the coil is 4 A If the magnitude of uniform magnetic induction B for the sphere to be in equilibrium K tesla then find K g 10 m s as shown in figure is 0 37 A Sphere m R 0 hr min B

2 1 A conducting rod of length L m is carrying a current I 1A as shown in the diagram It is made to move in a circular path of radius r m in a magnetic fiel B Bo r with 10 revolutions per minute Where B 3T and is a unit vector is radial direction If the power in watt required to make this rod move with a constar angular speed is P find the value of 10P AMIINIUM ZA r conducting rod

wo very long straight and parallel wires carry steady currents I and respectively The distance between the wires is d At a certain instant of time a point charge q is at a point equidistant from the two wires in the plane of he wires Its instantaneous velocity v is perpendicular to this plane The magnitude of the force due to the magnetic field acting on the charge at this instant is A 3 Holqu 2nd Holqu

A circular coil is made from a wire of length 1 m When a current A passes through it its magnetic moment is Am 4T m 16 Am T 1 Am TU

A long straight wire of radius R carries a steady current I The current is uniformly distributed over its cross section 2a The magnetic field at a distance from its centre is 3 Ho 2 a ta Ho 3 2 l

A ring of radius R and mass m is uniformly charged with charge Q It is rolling purely as shown A uniform magnetic field of magnitude B is present perpendicu plane of the ring If the normal force exerted by the ground is Amg find Take QvB mg 64

The magnetic force on a current carrying semi circular loop moving in a transverse magnetic field as shown in the figure will be X X X X BIR 2BIR 4BIR BIR 2 X X

The figure below shows a current loop having two semi circular arc joined by two radial lines The magnetic field at O is Hol 2R Ho 4R Hol 8R 2 R OR

4 none of these The magnetic susceptibility of a paramagnetic 7 substance at 73 C is 0 0060 then its value at 173 C will be 1 0 0030 2 0 0120 3 0 0180 4 0 0045 4 173 1 0 0030 2 0 0120 3 0 0180 4 0 0045 3 0 0060

A charge q moving with velocity vi enters a region of magnetic field B and electric field E If Eo Bovo then motion of charge particle will O Uniform circular motion O Helical motion with uniform pitch O Helical path with non uniform pitch O Uniformly accelerated motion along straight line

A very long wire ABDMNDC is showr figure carrying current I AB and BC parts straight long and at right angle At D w forms a circular turn DMND of radius R BC parts are tangential to circular turn at N D Magnetic field at the centre of circle is M Hol 2R N B A D Hol 2 x 1 2 R MIC

Magnetic Effect of Current fe n un face fay for alle an find the Magnetic field intensity L at the t o for CO B 1 a Ans a 2 a MOI 2R 1 1 1 1 0 Hol 12 1 1 Ans a 2R 2R 2 R OR 2 b 8 b H01 1 1 b PR b Hol 2R 2 T R a given current distribution

A particle of charge q 1 6 x 10 19 C and mass m 1 6 x 10 27 kg is projected from the origin with a velocity v 1 4 x 106m s at an angle 45 with the x axis as shown in the figure A uniform magnetic field 10 T k exists in the region Find the distance of the point where the particle will cross the x axis again 45

If a charged particle of charge is travelling with a velocity v in a magnetic field B then the force that that charged particle feels is given by F qvx B In this case the force F is also a vector quantity since it has both a magnitude and a direction So the cross product plays an important role in physics and engineering B Now suppose that a proton with some positive charge g is traveling in the 23 plane with a velocity in the direction of 3 and that the magnetic field B is a uniform field pointing straight up in the direction perpendicular to the zy plane Then the direction of the force that the moving proten feels is in the direction the vector V jen Note make sure to use Maple notation for the vectors e g 1 2 3 This is a direction which select all that apply C is perpendicular to the direction of the magnetic field is parallel to the direction of the magnetic field C is also in the 23 plane is perpendicular to the velocity of the particle Challenge worth 2 marks If we ohren this ticle for a Firmal the riniana

Figure 1 A Y is positive and X is negative B X and Y are at the same potential C X is positive and Y is negative f H 4 In Figure 1 two solenoids are in line The switch S initially opened is closed The polarity of the induced emf in terminals X and Y is

5 Two long straight parallel wires are 1 00 m apart as shown The wire on the left carries a paper current I1 6 00 A into the plane of the a What must the magnitude and direction of the current l2 be for the net magnetic field at point Q to be zero b Then what are the magnitude and direction of the net magnetic field at P c Then what is the magnitude of the net magnetic field at S Q 0 50 m 0 60 m I 6 00 A 0 80 m 1 00 m 0 50 m 12 P

14 20 cmf Figure 3 20 cm 45 10 cm 20 cm 13 3 A circular loop of radius 10 cm and three long straight wires carry currents of I 60 A 12 20 A 13 70 A and 14 30 A respectively as shown Each straight wire is 20 cm from the E 180 T center of the loop In Figure 3 the y component of the resultant magnetic field at the center of the loop is closest to B 100 T A 50 T D 80 T C 360 T 3

14 20 cm Figure 3 45 10 cm 20 cm 20 cm On 2 3 A circular loop of radius 10 cm and three long straight wires carry currents of I 60 A 12 20 A 13 70 A and I4 30 A respectively as shown Each straight wire is 20 cm from the E 180 T center of the loop In Figure 3 the y component of the resultant magnetic field at the center of the loop is closest to D 80 T A 50 T C 360 T B 100 T 3