Magnetic Field due to current Questions and Answers

Magnetic moment associated with an electron moving at speed vin a circular orbit of radius r is in magnitudes 1 evr 3 evr 4 2 NCERT Maps NCERT Pg 162 4 evr 2 ev

material of resistivity p The inner and outer radii of ring are a and 2a respectively and its thickness is h The ring is placed in a time varying magnetic field B kt where k is a constant which is parallel to the axis of the ring as shown in the figure The induced current in the ring is B kt A B C D a 2a 3kha 4p 3kha 2p 5kha 4p 5kha 2p h

7 Two long straight parallel wires A and B carrying current of 20 A and 10 A is same direction are separated by a distance of 5 cm The force of 15 cm section of wire B is NCERT Pg 173 1 1 5 x 10 N attractive 2 1 6 104 N repulsive

Charges and Magnetism In a chamber a uniform magnetic field of 1 2 T is maintained An electron is shot into the field with a speed of 3 2 x 10 m s 1 normal to the field The radius of circular orbit in which it starts circular path is m 9 1 x 10 31 kg INCERT Pg 169 1 15 16 m 2 6 27 m 3 12 42 m 4 22 4 m

Figure shows two long parallel wires separated by a distance of 18 cm There is current of 8 A in wire 1 and 12 A in wire 2 At what point on line joining of the wires the magnetic field is zero 8 A 18 cm 2 12 A O 5 2 cm from wire 1 9 4 cm from wire 2 O 7 2 cm from wire 1 O 10 3 cm from wire 2

iv A long cylinder of radius a carrying a uniform surface charge rotates about its axis with an angular velocity co Find the magnetic field energy per unit length of the cylinder inside of it if the linear charge density equals and consider permeability of the medium is equal to unity 2 2 2 8n

4 46 The magnetic moment of a short magnet is 8 Am What is the magnetic induction at a point 20 cm away on its equatorial line from its mid point A 10 4 Web m C 3 x 104 Web m B 2 104 Web m D 4x 10 4 Web m

Consider a metallic ring of radius 1m mass 1kg and carrying current 1A in a gravity free space in x y plane with its center at origin as shown If a uniform magnetic field 31 43 T is applied then instantaneous acceleration of point P which is on the y axis at the moment is n m s Find p Yip

5 Two particles A and B of masses m and me respectively and having the same charge are moving in a plane A uniform magnetic field exists perpendicular to this plane The speeds of the particles are vA and VB respectively and the trajectories are as shown in the figure Then 2001 2M JEW O Ao B O O O 0 a mAVA MB VB c m mB and v VB VA O O O O O O O b MAVA MBVB d m m and v VB

The ratio of magnetic field at the centre of the uniform coil of single turn due to arc abc and arc adc will be 1 I a B 4 B2 12 B 11 d 1 12 2 4 b B B2 B 1 2 1 1 2

5 If magnetic field at a point P x y z is given by B a x y k then the net force on loop shown in the figure is 1 ia abi abj 3 ia abi abj YA D A a B X 2 ia a i b j 4 ia a i b j

14 Two infinitely long straight wires lie in the xy plane along the lines x R The wire located at x R carries a constant current and the wire located at x R carries a constant current 12 A circular loop of radius R is suspended with its centre at 0 0 3R and in a plane parallel to the xy plane This loop carries a constant current in the clockwise direction as seen from above the loop The current in the wire is taken to be positive if it is in the direction Which of the following statements regarding the magnetic field B is are true ZNA JEE Adv 2018 Paper 1 A If 1 then B cannot be equal to zero at the origin 0 0 0 B If 0 and 0 then B can be equal to zero at the origin 0 0 0 for C If 0 and 0 then B can be equal to zero at the origin 0 0 0 D If I I then the 7 component of the magnetic field at the centre of the loop is Hol

TYPE questions Each question has 4 A conical container height h Radius of base R a spherical container Radius 3R and a cylindrical container height h Radius of base 2R each contain a charge Q inside them The ratio of respective electric flux through the containers will be All containers are closed O 1 2 3 O 1 1 1 Read More 3 2 1

0 The magnetic needle of tangent galvanometer is deflected at an angle 30 due to a magnet The horizontal component of earth s magnetic field is 0 34 x 10 4T along the plane of the coil Then the magnetic intensity will be 1 1 96 105 T 2 1 96 104 T

20 If declination at a place is known to be 15 E And a compass needle points as shown the geographic north is represented by the direction numbered 1 1 3 3 3 2 15 15 75 75 2 2 4

jual dipole moments M are fastened perpendicularly at their centres as shown below point P is in the plane of the magnets N 1 Ho M 4 d 1 S 2M d P The magnetic field magnitude at P distance d from the centre on the bisector of the right angle is P S N 2 M 2 Mo 4 d Ho 2 2M

Given fig shows cross section of two long straight wires The left hand wire carries current directly out of the page The net magnetic field due to the two currents is zero at point P then which of the following statements is correct 12 1 2 3 4 Current i2 is directed out of the page 1 12 i 12 None of these P

The radius of a circular coil is R and it carries a current of I ampere intensity of magnetic field at a distance x on the axis from the centre x R will be B Ho 1R 2 x2 B 440lR 2x3 B HolR 2x2 HolR 2x3

sliding on horizontal surface A uniform magnetic field B perpendicular to plane of the ring exist in the region Choose the correct option B A 000 B IVc Vgl IVc Vol OIVA Vd 2BW R DIVD Vgl 0 O

Two polaroids are placed in the path of unpolarized beam of intensity lo such that no light is emitted from the second Polaroid If a third Polaroid whose polarization axis makes an angle 0 with the polarization axis of the first Polaroid is placed between these polaroids then the intensity of light emerging from the last Polaroid will be 10 8 sin 20 10 4 sin 20 40

The coils A and B having radii in the ratio 1 2 carrying currents in the ratio 5 1 and have number of turns in the ratio 1 10 The ratio of magnetic inductions at their centres will be 1 2 1 2 1 1 3 4 1 4 1 4

Figure shows an electrical circuit which has a rectangula region of uniform and constant magnetic field B A long metallic sheet of width is being moved with velocity v Reading of galvanometer G will be O Zero Blv R Bvl 2R R www 114 xxxxx

An electron moving in the XY plane with 106 m s makes an angle of 60 with X axis There is a magnetic field of 10 2 Wblm directed along the Y axis Calculate the magnitude and direction of the magnetic force on the electron What will be the answer if the field is directed along ve Z axis

When is the field constant and zero nside the tube Q4 A hollow tube is carrying an electric current along its length distributed uniformly over its surface The magnetic field This question has multiple correct options A increases linearly from the axis to the surface B is constant inside the tube C is zero at the axis Correct Answer D Correct Answer is zero just outside the tube

Two wires are wrapped over a wooden cylinder to form two coaxial loops carrying currents i and i If i 8i the value of x for B 0 at the origin O is R R A 7 1 R C 3R L B 5R D 7R

A long straight wire of radius R carries a steady current 1 The current is uniformly distributed over its cross section The magnetic field at a distance from its 2a 3 centre is O Hol 2 a O Hol 3 240

If an electron of charge e is moving along X direction and magnetic field 1 point is along Z direction then the magnetic force acting on the electron will be along Option 1 a X axis b X axis c Y axis d Y axis

An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E The direction of electric field is now reversed keeping its magnitude the same A proton is allowed to fall from rest in it through the same vertical distance h The time of fall of the electron in comparison to the time of fall of the proton is NEET 2018 1 Smaller 3 Equal 2 5 times greater 4 10 times greater

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

The voltage of an source varies with time according to the equation V 100 sin 100 it cos 100 nt Where tis in second and Vis in volt then The peak voltage of the source is 100 volt The peak voltage of source is 50 volt The peak voltage of source is 100 2 volt The peak voltage of source is 100 2 volt

The initial phase angle for current 10 sin wt 8 co wt is tan tan sin 90 4 5 5 3 45

Infinite long strip of width 3 cm carrying current 10 A is placed in x y plane Magnetic field at a distance of 1 cm from strip at an outside point in x y plane is

In the circuit given below what will be the reading of voltmeter V wwww 300 V 900 V 200 V 100 V oooo 100 V 100 200 V 150 Hz

The strength of current in 1 H inductor changes at a rate of 2A sec Find the voltage across it and determine the magnetic energy stored in the inductor after 2 Sec A 2V 8 J B 4V 2 J YOU C O 2V 2 J

180 Mark for Review To obtain radial magnetic field in a moving coil galvanometer O The number of turns in the coil are increased O Poles are cut cylindrically 02 5 hr mi O Magnet is taken in the form of a horse shoe O Coil is wounded on aluminium frame

Example 1 8 A uniform constant magnetic field B directed tan angle of 45 to the x axis in the x y plane PQRS is a rigid quare wire frame carrying a steady current Io with its center at the origin O At time t 0 the frame is at rest in the position hown in Fig 1 100 with its sides parallel to the x and y axes Each side of the frame is of mass M and length L a What is the torque 7 about O acting on the frame due to the magnetic field b Find the angle by which the frame rotates under the action of this torque in a short interval of time At and the axis about which this rotation occurs At is so short that any variation on the torque during this interval may be neglected Given moment S P O Fig 1 100 R Q x

An electron enters a region where magnetic field B and electric field E are mutually perpendicular then O It will always move in the direction of B O It will always move in the direction of E O It always possesses circular motion

A long thin non conducting cylindrical pipe having surface charge density o radius R rotating with angular velocity kt about is axis where k is a positive constant Which of the following statement is are correct for inside region of pipe A Magnetic and electric field are uniform throughout region and do not vary with time B Magnetic field is constant throughout region but vary with time and electric field is not constant throughout region and independent of time C Magnetic field is not constant throughout region but independent of time and electric field is constant throughout region and vary with time D Energy density u due to magnetic field varies with time as u bt Where bis positive constant

33 A circular loop of radius R is moved with a velocity v as shown in the diagram The force needed to maintain its velocity constant is 2 20 2m a R HAR Real R

Two long conductors separated by a distance d carry currents I and I in the same direction They exert a force F on each other Now the current in one of them is increased to four times and its direction is reversed The distance is also increased to 4d The new value of the force between them is O F F 453 2F 3 G

An insulating thin rod of length 7 has linear charge density p x Po on it The rod is rotated about an axis passing through the origin x 0 and perpendicular to the rod If the rod makes rotations per second then the time averaged magnetic moment of the rod is On pol omd o In Po

wire of infinite length carrying current has along the z axis A square loop of side is placed such hat the plane of the loop makes an angle 74 with the positive x axis at 0 0 and side AB touches e x axis and parallel to z axis as shown in the figure The magnetic flux passing through the loops Find the value of k Given 10 A In1 6 0 47 and tan37 3 4 H 74 1 0 0 Correct answer 02 35

A long straight wire carries a current along the x axis Consider the point A 0 1 0 B 0 1 1 C 1 0 1 and D 1 1 1 Which of the following pairs of points will have magnetic field of the same magnitude A and B A and C B and C B and D

28 The interference pattern is obtained with two coherent light sources of intensity ratio 4 In the min will be max interference pattern ratio max 1 4 3 3 8 9 29 Which voltmeter will give non zero reading at resonance 1 Only V 3 Both V and V3 V 1 30 A non conducting disc of radius R charged uniformly over one side with surface charge density rotate about its geometrical axis with an angular velocity The magnetic moment of the disc is COMGR 3 OMGR 2 B 2 1 9 4 5 4 R B D 2 Only V 4 Both V and V 3 4 MGR 31 The magnetic susceptibility of a magnetic material at 227 C is 0 00002 Then magnetic susceptibility of material at 727 C will be D 1 0 00002 2 0 00004 3 0 00001 4 0 00008 32 All straight wires are very long Both AB and CD are arcs of the same circle both sub tending right angles at the centre O Then the magnetic field at O is o 2 CONGR A 1 J 3 Ho 4xR 1 2TR 33 In a plane electromagnetic wave the electric field oscillates sinusoidly at a frequency of 2 x 1010 Hz and amplitude of 48 V m The frequency of oscillation of magnetic field will be 1 2 x 100 Hz 2 16 10 Hz 3 3 2 x 100 Hz 4 16 x 100 Hz 34 A charge Q is situated at the corner of the cube The electric flux through the cube will be o o 2 2 1 sin 3 4TR Hoi 4 x 1 2nR NIE 8 35 The capacity of a parallel plate capacitor depends on 1 The metal used to make the plate NIE 2 2 The thickness of the plates 3 The potential applied across the plates 4 The separation between the plates 36 A prism of refractive index u and refracting angle A is placed in the minimum deviation position If the angle of minimum deviation is A then the value of A in term of u is 2 sin 1 Spherical 3 Cylindrical Q 4 2 3 2 cos 4 cos 37 The magnifying power of an astronomical telescope for normal adjustment is 10 and the length of telescope is 110 cm The magnifying power of the telescope when image is formed at the least distance of distinct vision is 1 14 2 48 3 28 4 52 38 The condition of observing Fraunhalfer diffraction from a single slit is that the wavefront incident on the slit must be NIE 2 Elane 4 Elliptical

de A 3 The magnitude of uniform magnetic field in a small region of Helmholtz coils is nearly N is number of turns in each coil 2 1 HONI 2R 3 2 NI R 4 HNI R 0 72 NI R 10

A circular coil of 30 turns and radius 8 cm carries a current of 6 A It is suspended in a uniform horizontal magnetic field of 1 0 T The field lines make an angle of 60 with the normal of the coil The magnitude of counter torque that must be applied to prevent the coil from turning is NCERT Pg 169 1 3 133 N m 2 0 236 Nm 3 30 8 Nm

certain region uniform electric field E and magnetic field B are present in the opposite direction At the instant t 0 a particle of mass m carrying a charge q is given velocity v at an angle 0 with the y axis in the yz plane The time after which the speed of the particle would be minimum is equal to X 3 10 E KY mvo qE mv cose 0 B B D Z mv sine qE 2 m

i ii State Biot Savart law A current I flows in a conductor placed perpendicular to the plane of the paper Indicate the direction of the magnetic field due to a small element dat point P situated at a distance from the element as shown in the figure 2

e 16 Write equation for Ampere s circuital law for the Amperian loop shown traversed in the direction shown by arrow marks put on it 1 2 If seen from top left side portion of the loop is traversed anticlockwise while the other portion is traversed clockwise Thus by sign convention i is positive i is positive i is negative Thus B d Mol Ho 1 12 13

A solenoid core material has relative permeability 400 Windings of solenoid are insulated from core and carry a current of 2 A If number of turns are 1000 per metre what is the magnetic field Bat centre of solenoid 1 0 T 3 99 T 2 0 T 08T