Magnetic Field due to current Questions and Answers

Iwo thick wires and two thin wires all of the same material and same length form a square in three different ways A B and C as shown in the figure With correct connections shown the magnetic field at the centre of the square is zero in case of 1 A only 3 B C only Current I A B 2 4 A B only A C only C

Four rods each mass m and length are arranged in form of rectangle as shown in the figure The moment of inertia about perpendicular bisector of opposite sides is 1 me mil 2 6

A current is flowing in a vertical wire in downward direction the direction of magnetic field of a point which is just right side to the wire 1 towards north 2 towards south 3 towards east 4 towards west

A circular coil carrying a certain current produces a magnetic field B at its centre The coil is now rewound so as to have 3 turns and the same current is passed through it The new magnetic field at the centre is 2 9B 1 Bo 9 Bo 3 4 3B 14 The magnetic field at the centre of a current carrying circular coil of radius 10 cm is 5 5 times the magnetic field at a point on its axis The distance of the point from the centre of the coil in cm is

A point charge of 6 C is placed at a distance 20 cm directly above the centre of a square of side 40 cm The magnitude of the flux through the square is

Current through the conductor PQ in the given diagram is 1m 202 1 2A from P to Q 3 4A from P to Q P 2m s B 2T 2 2A from Q to P 4 4A from Q to P

A long straight wire along z axis carries a current in the negative z direction The magnetic field vector B at a point having co ordinate x y in z 0 plane is 1 3 Hol yi xi 2 x y Hol xj yi 4 x y 2 4 Hol xi yi 2 x y Hol xi yi 2 x y

A square frame of side carries a current i The magnetic field at its centre is B The same current is passed through a circular coil having the same perimeter as the square The field at the centre of B the circular coil is B The ratio of B 1 2 3 4 8 2 TC 8 2 3 TU 8 2 TU 4 2 2 is

A rod of length 1 1m and resistance R 100 is being pulled with a constant velocity of 4m s towards right At time 1 0 the rod is 1m away from left end The magnetic field is B 1 31 T Find work done in J by the external agent to move the rod with constant velocity for first 5sec the rest of circuit is resistance less Neglect friction 4 point

A uniform magnetic field of 0 5 gauss exists in a region A long straight wire carrying a current of 10A is placed in the region such that the direction of current is parallel to the external magnetic field The resultant magnetic field induction at a point 10 cm away from the wire is 1 9x 10 5 T 2 41 10 5 T 3 7 10 5 T 4 29 10 5 T

Figure shown two long straight wires carrying electric currents in opposite directions The separation between the wires is 5 0 cm Find the magnetic field at a point P midway between the wires 10 A P 10 A

Matter Example 5 5 Figure 5 5 shows a small magnetised needle P placed at 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 9 1 Ofp 9

The magnetic field due to current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from centre is 54 T The value of magnetic field at centre of loop is 1 250 uT 2 150 HT

4 As shown in diagram a current carryin conductor is subjected to steady uniform magnetic field Then 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

3 A wire bent into a regular polygon of n sides is inscribed in a circle of radius a If a current I passes through the wire and the polygon is placed in a uniform magnetic field B with its plane perpendicular to the field The net force experienced by the regular polygon is 3 1 1 B tan n 2 2 T B tan a 3 3B 12 2 a T tan a 4 Zero

agnetic eld of strength B perpendicular to its plane Radius of loop is r current in the loop is i and linear mass density of loop is m Speed of any transverse wave in the loop will be 1 Bir m 2 Bir 2m

of charge q and mass m enters a uniform magnetic field B at A with speed v at an angle a and leaves the field at C with speed v at an angle as shown Then V A X AX ayo X X Cl x X X X X X X X X X X X 1 2 V V 3 Particle remains in the field for time t All of these 2m qB

1 A massless square loop of side carrying current i is suspended from a pulley as shown in the arrangement Lower edge of the loop is in transverse magnetic field B The minimum current i required in the loop to just move the block of mass m up the inclined plane is 0 H xx xxx xxx xxx 1 B

Same current i 2A is flowing in a wire frame as shown in figure The frame is a combination of two equilateral triangles ACD and CDE of side 1m It is placed in uniform magnetic field B 4T acting perpendicular to the plane of frame The magnitude of magnetic force acting on the frame is A 1 24 N X X X X 2 Zero X X

0 A magnet is suspended in the magnetic meridia with an untwisted wire The upper end of wire rotated through 181 to deflect magnet by 3 from magnetic meridian Now this magnet replaced by another magnet and upper end wire has to be rotated by 273 to deflect magn by 53 from magnetic meridian The ratio magnetic moment of the two magne respectively is 1 3 3 m 2 4 48 55 181 273

S spin angular momentum S and orbital angular momentum 1 associated with the intrinsic respectively of an electron are predicted by quantum theory and verified experimentally to a high accuracy to be given by H e m S e 2m 1 Which of these relations is in accordance with the result expected classically Outline the derivation of the classical result

A particle of charge Q and of negligible initial speed is accelerated through a potential difference of U The particle reaches a region of uniform magnetic field of induction B where it undergoes circular motion If potential difference is doubled and B is also doubled then magnetic moment of the circular current due to circular motion of charge Q will become a double c four times b half d remain same Her

9 Two long parallel metallic wires with a resistance R form a horizontal plane A conducting rod AB is on the wires shown in figure The space has magnetic field pointing vertically downwards The rod is given an initial velocity v There is no friction in the wires and the rod After a time t the velocity v of the rod will be such that A R S OB D Vo

A cyclotron is used to accelerate protons H Deuterons H and a particles He While exiting under similar conditions the minimum K E is gained by A proton B deuteron C same for all a particle

3 14 The magnetic field at the centre of a current carrying circular coil of radius 10 cm is 5 5 times the magnetic field at a point on its axis The distance of the point from the centre of the coil in cm is 1 5 2 10 3 20 4 25 15 Same current is flowing in three infinitely long wire along positive x y and z directions The magnetic field at a point 0 0 a would be

Find force per unit length at P 5A C 10 cm P a 104 m c 3 x 104N m D b 10 Nm d 0 3 Nm A

12 Two similar loops of radius R are lying concentrically with their planes at right angles to each othe The currents flowing in them are and 3 respectively The magnetic field at the centre of the coil is S 2R 4 l R 2 4 Mol R 3 ol R

is projected from A in nonuniform magnetic field as shown in figure A B XID X 5x10 The magnitude of velocities at point A B and C respectively during the motion is 1 Maximum at A and C 2 Maximum at B 3 Minimum at A and C 4 Equal at A B and C I JK 1 1 0 6 0 4

Try Yourself 11 Find B al over following loops direction in which integration has to be performed is indicated by arrows 4 het b NV Curront Carrying Wire

A large metal sheet carries an electric current along it surface Current per unit length is A Magnetic field nea the metal sheet is O O O O O ooooo a 102 4402 c 2 b d 2 o 2x Ho 22x

A wooden stick of length 3 is rotated about an end with constant angular velocity in a uniform magnetic field B perpendicular to the plane of motion If the upper one third of its length is coated with copper the potential difference across the whole length of the stick is 9Bol a b c d 2 4Bwl 2 5Bol 2 Bol 2 X X X X X X X X X X X Xx x x x3l X XX X X X X XV X X X X X X X X X X X X X X X X X X Tricky w X copper X coat X X X X X XX XX X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 1

Two long fixed parallel thick rails are lying in a region having uniform magnetic field perpendicular to the plane of the rails Two identical sliders of mass m and resistance R each initially at rest can slide over the rails If one of the slider is given velocity Vo the velocity of the other slider after considerably long time will be Neglect friction 2 A Vo C v 2 B zero D v 4 IN Je 12 OB Vo Blv

For the given current distribution the magnetic field at point P is 5A4 1 O Ho 4 2 5m P K 5m Ho T 2 2 5A 3 Ho 2 Ho 4 MOT 2 O 61

A circular current loop is shown in the adjacent figure The magnetic field in the region is along x axis and its magnitude in the space is increasing with increasing y coordinate The net magnetic force on the loop is A along z axis C along y axis B along z axis D zero Y 201 X

A vertical wire carries an electric current into the page An electron approaches the current from east What is the direction of the magnetic force on the electron N W

16 If B B and B are the magnetic field due to 1 12 and 3 then in Ampere s circuital law B di Mol Bis 01 01 2 1 B B B 3 B B B B 01 73 2 B B B B 4 B B

for paramagnetic substances is valid 1 above curie temperature 2 below curie temperature 3 Above magnetic saturation 4 below magnetic saturation 34 A in

3 An ionized gas contains both positive and negative ions If it is subjected simultaneously to an electric field along the x direction and a magnetic field along the z direction 2000 2M then a positive ions deflect towards y direction and negative ions towards y direction b all ions deflect towards y direction c all ions deflect towards y direction d positive ions deflect towards y direction and negative ions towards v direction

D A very small coplanar at the centre of a square wire of dimension The mutual inductance between the loops is 1 2 3 2 2 or 2 2 or 1 2 2 r 1

5 A solid current carrying conductor of radius R is having current per unit area J as J ar R where a is a constant and ris distance from axis Find magnetic field at distance x from axis of wire Assume x R 3 HaR 3x HaR X 2 HaR 2x 4 Zero ar

A symmetric star shaped conducting wire loop is Carrying a steady state current I as shown in the figure The distance between the diametrically opposite vertices of the star is 4a The magnitude of the magnetic field at the center of the loop is JEE Main 2017 a Ho6 3 1 4 c Hol3 2 3 4 b d 4 a Hol 6 3 1 4 na Hol 3 3 1 4

The oscillator frequency of a cyclotron is 10 MHz What should be the operating magnetic field for accelerating proton 1 0 156 T 3 0 356 T 2 0 256 T 4 0 656 T

D An electron enters in a viscous medium having uniform perpendicular magnetic field due to which it moves in spiral path of decreasing radii Its angular momentum 1 Increases 2 Decreases 3 Remains constant

An a particle experiences a force of 3 84x10 14 N when its moves perpendicular to magnetic field of 0 2 Wb m then speed of the a particle is 1 6 0 x 105 m sec 2 5 0 x 105 m sec 3 1 2 x 106 m sec 4 3 8 x 106 m sec

F A long straight hollow conductor tube carrying a current 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 B a B B B b B B B3 2 c B B B3 d B cannot be found unless the dimensions of the

A ring of radius 10 cm carrying current 2A placed in horizontal plane in uniform magnetic field in such a way that field makes an angle 30 with vertical direction Magnitude of magnetic field at each point of ring is 350G magnetic force on ring is 1 0 01 N 3 0 02 N B cos30 B B sin 30 2 0 05 N 1 4 0 04 N

3 1 Ho 3M 4 r 2M Mo Ho 2M 41 Magnetic field induction at P which is equidistant from centres of three short magnetic dipoles is 2 N 4 Z N S 2M Mo M 4x r S N 4M

4 2 3x10 T The magnetic moment of a short bar magnet is 2 Am The magnetic field at a point 1 m away from it in a direction making an angle 60 with its magnetic moment is 1 5x10 T 2 10 7 T 3 7x10 7 T 4 7X10 T

A conducting rod AB of mass m and length is supported by conducting massless wires and carrying a current I as shown in the figure The rod is slightly displaced into the paper such that rod always remains parallel to x axis and released to perform SHM If its time period is 1 4 2 ka V g 1 Ble mg 2 Find the value of k B y x a A m I l a B

Illustration 2 Energy from the sun falls on the earth at a rate of 1353 W m2 Which is known as solar constant i e the power incident per unit area per unit second at the top of atmosphere Find the rms values of the electric and magnetic fields in the sunlight reaching the top of the atmosphere