Magnetic Field due to current Questions and Answers

A oll Of has negligible resistance As sh in the schematic figure its two ends are connected to two wires and it is hanging by those wires with its plane being vertical The wires are connected to a capacitor with charge Q through a switch The coil is in a horizontal uniform magnetic field B parallel to the plane of the coil When the switch is closed the capacitor gets discharged through the coil in a very short time By the time the capacitor is discharged fully magnitude of the angular momentum gained by the coil will be assume that the discharge time is so short that the coil has hardly rotated during this time a 7 2 NQB R b 7NQB R B

63 A tuning fork of frequency N is sounded at the open end of a long cylindrical tube having a side opening and fitted with a movable reflection piston At a certain position of the piston the listener hears a maximum sound as shown in the figure When the piston is moved through 9 cm the intensity of sound becomes minimum If the speed of sound is 1 360 ms the value of N is E a 250 Hz b 500 Hz c750 Hz d 1000 Hz Ear

A metallic rod of length is rotated in a horizontal plane with an angular velocity w where no magnetic field exists If emf induced in the rod charge and mass of electron is e and m respectively is mw e Ne 3 then value of Nis A

The figure below shows two wires each carrying a current The first wire consists of a circular arc of radius Re0 37m and two equal radial lengths of L 0 75R it carrie current f1 8 4A The second wire is long and straight it carries current 12 4 5A and it is at distance d 0 5R from the center of the arc At the instant shown a snapsht of a charged particle of charge q moving at velocity v 48 17 m s toward the straight wire Find the magnitude of the magnetic force on the charged particle due to the wires in terms of quo Express your final result using zero decimal places R V 3x 45 19

A very long thin rod carries electric charge with the linear density 42 0 nC m It lies along the x axis and moves in the x direction at a speed of 1 50 x 107 m s a Find the electric field the rod creates at the point x 0 y 20 0 cm z 0 magnitude 3777 N C direction y axis b Find the magnetic field it creates at the same point magnitude 6 3e 07 direction z axis c Find the force exerted on an electron at this point moving with a velocity of 2 40 x 108 m s 6 24e 16 x Your response is within 10 of the correct value This may be due to roundoff error or you could have mistake in your calculation Carry out all intermediate results to at least four digit accuracy to minimize roundoff error N magnitude

A Zero B HORJ C HORJ D 3 4 HORJ 2R 31 The diagram above shows the cross section of a long cable that has an inner wire of radius R surrounded by a conducting sheath of outer radius 2R The wire and the sheath carry currents in opposite directions but with the same uniform current density J What is the magnitude of the magnetic field at the surface of the outer conductor E RJ X X X

1 A rectangular coil 400 turns dimensions 0 1 m X 0 2 m is rotating in a uniform magnetic field B 0 2 T At t 0 s the normal to the coil is perpendicular to the magnetic field Att 0 02 s the normal makes an angle of p 60 with the field An average current of magnitude 4 A is induced in the coil Find the resistance of the coil

A generator feeds power to an infinite bus through a double circuit transmission line A 3 phase fault occurs at the middle point of one of the lines The infinite bus voltage is 1 pu the transient internal voltage of the generator is 1 1 pu and the equivalent transfer admittance during fault is 0 8 p u The 100 MVA generator has an inertia constant of 5mJ MVA and it was delivering 1 0 p u power prior of the fault with rotor power angle of 30 The system frequency is 50 Hz If the initial accelerating power is X pu the initial acceleration in elect dag sec and the inertia constant in MJ sec elect deg respectively will be

A magnet is made to oscillate with a particu frequency through a coil as shown in figure The time variation of magnitude of emf generated across the coil during one cycle is 1 3 e voooooo www mm fr 2 eA eA 4 eA he

Figure shows cross section view of infinite cylindrical wire with a cavity current density is uniform jok X A magnetic field inside cavity is uniform B magnetic field inside cavity is along a C magnetic field inside cavity is perpendicular to a q no10

as shown in figure Match the following 1 1 2 20 Q i 152 2 AR 450 Table I A Magnetic field at P B Magnetic field at Q 1 A P B Q S P Q R B N 2 2972 Table II NOX A 2TR S inwards outwards Ho i 2 r No 271K Ni 2TR Ni 2712 Ho 4x r 2 A P S B Q S

A wire bent as shown in fig carries a current i and is placed in a uniform field of magnetic induction B that emerges from the plane of the figure Calculate the force acting on the wire O OO OIO

An electron at point A in the Figure has a velocity v 10 ms Then if e 1 6 x 10 1 9 C AB 10 cm and m 9 1 x 10 1 kg L A magnitude of magnetic induction that will cause the electron to follow the semicircular path from A to B is 1 13 mT B time taken to go from A to B is 1 57 10 s C angular momentum of the electron about A when t 0 785 x10 7s is 4 5 x 10 24 kgm s 3 D angle made by the velocity vector with the x axis at t 8 T is TL 4 rad

An infinitely long conductor is bent into an L shape as shown in Figure below If a direct current of 5 A flows in the conductor find the magnetic field intensity at a 2 2 0 b 0 2 0 and c 0 0 2 Take the origin at the bend y 5 A A

C 2 1 4 21 Figure 4 220 shows a charged particle of mass 2g and charge 5 C enters a circular region of radius 10cm in which there is a uniform magnetic field of strength 4T and directed perpendicular to the plane of circular region in the figure If the particle velocity vector rotates through 90 angle in passing through this region then its speed is A 0 25 mm s C 1 cm s C Figure 4 220 B 4 mm s D 1 mm s

24 A regular tetrahedron frame is made up of homogeneous resitance wire of uniform cross section Current I enters vertex A through a long straight wire directed towards the centre O of the tetrahedron and is conducted away through vertex B in the same way as in the figure Choose correct statement s illustrated D B There is no current through wire DC because point D and C are equipotential B Current through wire AB is I 2 Current through wire AC is I 4 SROOM D Net magnetic field at point O is zero 25 In the given circuit the point A is 9 V higher than point B Which of the following statements

A magnetic needle is free to rotate in a vertical plane which makes an angle of 60 with the magnetic meridian If the needle stays in a direction making an angle of tan 1 with the horizontal The true dip at that place is 37 53 30 60

There are two coils A and B as shown in figure coil B is fixed A current starts flowing in B as shown when A moves away from B and stops when A stops moving We can refer that A B O There is a constant current in the counter clockwise direction in A There is a constant current in the clockwise direction in A There is a varying current in A in counter clockwise direction There is no current in A

horizontally and is free to rotate about its axis as shown in the figure A strong magnet is held vertically at a point above the disc away from its axis On revolving the magnet about the axis of the disc the disc will the figure is schematic and not drawn to scale S N a rotate in the direction opposite to the direction of magnet s motion h rotato in the direction on the direction of magno notion

4 58 Find the force experienced by a pole of strength 100Am at a distance of 20cm from a short bar magnet of length 5cm and pole strength of 200Am on its axial line Ans 2 5 x 10 2N

Assertion A The Coulomb force between two points charges depend upon the dielectric constant of the intervening medium Reason R Coulomb s force varies inversely with the dielectric constant of medium A A B B C C

4 41 A long straight wire along the z axis carries a current I in the negative z direction The magnetic vector field B at a point having coordinates x y in the z 0 plane is A C Mol yi xj 2n x y Mol xj yi 2 x y B D Mol x yj 2 x y Mol xi yj 2 x y

A long straight wire carrying a constant current creates a magnetic field around it The magnetic field strength is measured with a magnetic field sensor at varying distances from the wire while the current is kept constant Which of the following indicates a graph that will have a constant positive slope and the Maxwell equation most closely related to the graph A B D E A graph of the magnitude of the magnetic field as a function of the current This is related to Faraday s law A graph of the magnitude of the magnetic field as a function of distance from the center of the wire This is related to Faraday s law A graph of the magnitude of the magnetic field as a function of distance from the center of the wire This is related to Ampere s law A graph of the magnitude of the magnetic field as a function of the inverse of the distance from the center of the wire This is related to Faraday s law A graph of the magnitude of the magnetic field as a function of the inverse of the distance from the center of the wire This is related to Ampere s law

When the two magnets are moved perpendicular to plane of coil as shown then ares a emfis induced b Induced current flows from A to Balong the coil when A and B are connected through resistor c Electrons flow from B to A along the coil d Hence plate A will become negatively charged and plate B becomes positively charged

of 10 4N m is required to hold a magnet at 90 with the horizontal component of the earth s magnetic field Torque required to hold it at 30 is 0 4Nm 4Nm thim

A cyclotron s oscillator frequency is 10 MHz If the radius of its dees is 60 cm what is the kinetic energy of the proton beam produced by the accelerator Given e 1 60 10 19 C m 1 67 x 10 27 kg 1 MeV 1 6 10 13 J O 3 421 MeV O 4 421 MeV O 5 421 MeV

A current carrying coil is subjected to a uniform magnetic field The coil will orient so that its plan becomes O O inclined at any arbitrary angle to the magnetic field O parallel to the magnetic field O perpendicular to the magnetic field inclined at 45 to the magnetic field

Statement 1 The magnetic field on the axis of a solenoid is non uniform Statement 2 When a charged particle is projected along the axis of current carrying solenoid the path of the particle is not changed O O O O Statement 1 is True Statement 2 is True Statement 2 is a correct explanation for Statement 1 Statement 1 is True Statement 2 is True Statement 2 is NOT a correct explanation for Statement 1 Statement 1 is True Statement 2 is False Both statements are False

A particle of mass m and charge q enters a region of magnetic field with speed v as shown in the figure If collision of particle with wall is elastic then time after which velocity of particle becomes antiparallel to its initial velocity is d X X m q V t 0 X X 1 X x Y m x X X x X x x x x m x 4 2q B x 3 2 x X B x x x x X x no magnetick field X X X X d 2 M 4qB m mv 2qB wall x 2 4 2 11

A hollow cylindrical wire of inner radius a and outer radiu b carries current i as shown in figure If the current density is uniform across its cross section the magnetic field at point P such that a r b is b a Hoi r a 2 b a r Moir 2 b a Hoiab 27 b a r

Two parallel long straight conductors are placed perpendicular to a metre scale in same plane at the 2 cm and 6 cm marks They carry current and 3 respectively in same direction The net magnetic field due to them wi be zero At the 8 cm mark At the 1 cm mark At the 5 cm mark At the 3 cm mark

A rod of length 2a is free to rotate in a vertical plane about a horizontal axis O passing through its midpoint A long straight horizontal wire is on the same plane and is carrying a constant current i as shown in figure At initial moment of time the rod is horizontal and starts to rotate with constant angular velocity w calculate emf induced in the rod as a function of time Okw

Current flows in a cylindrical conductor of radius R with uniform current density J over it s cross section A long R cylindrical cavity of radius is made in it such that the axis of cavity is parallel to the axis of conductor at a separation of The energy in the cavity per unit length is R 2 X MotJ R4 512 Ho TW R4 256 J R 256 J R4 120

The space has electromagnetic field which is given as B B k and E E k A charged particle having mass m and positive charge q is given velocity vi at origin at t 0 sec The z coordinate of the particle when it passes through the z axis is neglect gravity through motion 47 mE B A 27 mE qB qB C mE qB 2 D 4 mE qB 0

i Two small and similar bar magnets have magnetic dipole moment of 1 0 Am each They are kept in a plane in such a way that their axes are perpendicular to each other A line drawn through the axis of one magnet passes through the center of other magnet If the distance between their centers is 2 m find the magnitude of magnetic field at the mid point of the line fore

i AiA small fixed current carrying circular coil of 10 turns carrying current I having radius r lies in a horizontal plane at centre of a square loop having current I and edge length d r The force acting on the coil due to two adjacent sides of the square is Nuolir 2 Newton Find N

4 8 Consider a wire carrying a steady current I placed in a uniform magnetic field B perpendicular to its length Consider the charges inside the wire It is known that magnetic forces do no work This implies that a motion of charges inside the conductor is unaffected by B since they do not absorb energy b some charges inside the wire move to the surface as a result of B c if the wire moves under the influence of B no work is done by the force d if the wire moves under the influence of B no work is done by the magnetic force on the

a Irms lo c Irmis 10 T To are related as 1994 b Irms 2 10 d Irms 1 2 1994 68 An series L C R circuit is connected to a source of A C current At resonance the phase difference between the applied voltage and the current in the circuit is a T b zero d 2 c 4 1994 09 Two cables of copper are of equal lengths One of them has a single wire of area of cross section A while other has 10 wires of cross sectional area A 10 each Give their suitability for transporting A C and D C a only multiple strands for A C either for D C b only multiple strands for A C only single strand for D C c only single strand for D C either for A C d only single strand for A C either for D C 1994 70 If N is the number of turns in a coil the value of self inductance varies as b N d a N c 1993 75

A magnetic field B Boj exists in the region B a x 2a and B B in the region 2a x 3a where B is a positive constant A positive point charge moving with a velocity vi where v is a positive constant enters the magnetic field at x a The trajectory of the charge in this region can be like A 1 B KR H 2a a 3a 3 3a F

current carrying wire AB with current i is placed as shown in figure Find the magnetic field at orig Y 0 01 Molo TO 0 49 olo 0 3 A B 4 0 2 4 0 15 olo TC Mojo TC

36 A bar magnet is oscillating in a magnetic field and its frequency is 10Hz If another identical piece of brass be placed over that magnet the frequency of that combination in that field is 1 20 Hz 2 10 Hz 10 3 Hz 2 4 10 2 Hz

Please explain the lines in the brack ets in detail in the picture attached How is the principle of relativity relat ed to faradays law even if the charges are stationary land the q vx B term of the Lorentz force is not operativel an emf is nevertheless induced in the presence of a time varying magnetic field Thus moving charges in static field and static charges in a time varying field seem to be symmetric situation for Faraday s law This gives a tantalising hint on the relevance of the principle of relativity for Faraday s law The motion of a copper plate is damped when it is allowed to oscillate between the magnetic pole pieces How is the damping force produced by the eddy currents

A wire of fixed length is bent in the shape of a circle of single turn If a current flows in the circular loop then the magnetic field at the centre of the loop was found to be equal to B Now the number of turns in the loop are increased to 3 and the current is reduced by a factor of 3 The magnetic field produced at the centre of the loop will be B 3 B14 9 B

The electric field of a plane electromagnetic wave is given by E Ecos cos kz ot At t 0 a positively charged particle is at the point x y z 0 0 1 If its instantaneous velocity at t 0 is uo k the force acting on it due to the wave is 1 zero 2 parallel to 2

B C 1 k in a region of space between x 0 to x L as shown in figure A particle of mass m and positive charge q enters in this regions at origin While entering and leaving it make angles with planes parallel to YZ as and 2 respectively Motion of charge particle is confined to XY plane The relation 2mv cos 0 cos 0 AqLC satisfies the above condition find the value of X YA 0 7 0

circular loop rotating in a uniform 7 4x10 2 T magnetic field Figure 1 Figure B Pivot X Figure Circular loop 1 of 1 The figure is an edge on view of a 14 cm diameter circular loop rotating in a uniform 7 4x10 2 T magnetic field Figure 1 1 of 1 Y Part A What is the magnetic flux through the loop when is 0 Express your answer with the appropriate units Part B Submit Request Answer Y Part C 6 LOW Value Submit A Part D What is the magnetic flux through the loop when is 30 Express your answer with the appropriate units Submit Request Answer Value A HA Value What is the magnetic flux through the loop when is 60 Express your answer with the appropriate units C Request Answer Units Units Units What is the magnetic flux through the loop when is 90 Express your answer with the appropriate units

2 kg of ice at 20 C is mixed with 5 kg of water at 20 C The water content of the final mixture is Latent heat of fusion 80 kcal kg specific heat of water 1 kcal kg C specific heat of ice 0 5 2003 kcal kg C A 7 kg C 4 kg B 6 kg D 3 kg

Below is a loop fashioned from portions of a circular loop of radius R and a square loop of side length 2R 01 00 R R If the loop carries current I what is the magnitude of the magnetic field at point O 00 2375 01 R 00 3967 01 R

A charged particle enters a uniform magnetic field at some angle The particle will be deviated from its path by angle 180 Value of 0 will be X X X X X 1 90 3 120 q 0 X X X X X X X X X X X X X X X 2 60 4 180

3 75 A square wire of length 1 mass m and resistance R slides without friction on parallel conducting resistance rails as in Fig 13 19 The rails are inter connected at the bottom by resistance rails so that R the wire and rails form a closed rectangular loop The plane of the rails is inclined at an angle with the horizontal and a vertical uniform magnetic field B exists within the frame Show that the wire acquires a steady velocity of magnitude V g 13 19 mgR sin 0 B 1 cos 0 OOO O O B