Introduction to Magnets and Magnetic Field of Earth. Is the Geographical North pole of Earth also its Magnetic North pole ? Are there Magnetic Monopoles like electric charges ?

A magnetic needle is kept in a non-uniform magnetic field. It experiences

a) a force and a torque

b) a force but not a torque

c) a torque but not a force

d) neither a force nor a torque

Can Electric Field affect a Magnet ? Can Magnetic Field affect an electric charge ?

Magnetic Force on an electric charge moving in a Magnetic field. Can Magnetic forces do any work ?

i) A charged particle of mass 1 mg and charge q = +1 mC has velocity

v = 2 i + 1 j - 3 k. Find out the magnetic force on the particle and its acceleration at this instant due to magnetic field B = -2 i + k.

Is there any way to validate the answer ?

ii) A charged particle has acceleration a = 3 i + A j in a magnetic field

B = - 2 i + 3j + k. Find the value of A.

A particle with charge q = - 1 mC is moving in a uniform magnetic field B = 1k Magnetic force on the particle is measured to be F = 4 N i - 3 Nj

a) Find all components of velocity of particle you can from this information

b) are there any components of velocity that cannot be determined ? Explain

c) Calculate the scalar product of F and v , and F and B ?

A particle with charge q = 1 mc is moving with velocity v = 3 x 106 k in a uniform magnetic field.

The magnetic force on the particle is measured to be F = - 2i + 4j

a) Find all component of magnetic field you can form this information

b) b) are there any components of magnetic field that cannot be determined ? Explain

c) Calculate the scalar product of F and v , and F and B ?

Circular Motion of a charged particle moving in a Magnetic field perpendicular to its velocity. Most books use Fleming?s Left Hand Rule to relate the directions of velocity, magnetic field and magnetic force. Discover a simpler and more intuitive Right Hand Rule for relating the directions of Velocity, Magnetic Field and Magnetic Force.

A charged particle having mass 0.1 mg and charge 1 mc is projected with a speed of 1 km/s in a direction perpendicular to a uniform magnetic field of magnitude

1 T. Find

a ) the force acting on the charged particle,

b ) radius of the circular path

c ) time period with which it circulates in a circle,

d ) the angular velocity of the charged particle,

e ) its linear momentum,

f ) angular momentum and

g ) kinetic energy of the particle.

A neutron, a proton, an electron and an alpha particle enter a region of magnetic field with equal velocities. The magnetic field is inwards to the plane of the screen. The tracks of the particles are labelled in figure.

Mark the track of each particle.

There are 4 charged particles with their charge and mass as shown. The particles enter a magnetic field of strength B, perpendicular to the field.

What is the ratio of their

i) radius of circular path

ii) time period, if they have

Two particles having equal charges, enter a region of uniform magnetic field and describe circular paths of radii r1 and r2 respectively. What is the ratio of their masses, if initially,

a) their speeds are equal

b) they are accelerated through same potential

c) they have same momentum

Two particles A and B of masses mA and mB 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 fig. Then

a) mA vA < mB vB

b) mA vA > mB vB

c) mA < mB and vA < vB

d) mA = mB and vA = vB

A particle having charge q, initially at rest, is accelerated through a potential difference of V. It passes through a uniform magnetic field and experiences a force F. If the accelerating potential is increased to 2 V, force on the particle will be

a) F b) F/2 c) 2 F d) 2F

Also, how many times the potential difference should increase to double the force experienced by the particle ?

a) 2 b) 4 c) 3 d) 5

A charged particle is moving in a horizontal circle on a frictionless table by attaching it to a string fixed at one end. If a magnetic field is switched on in the vertical direction, the tension in the string

a) will increase

b) will decrease

c) remains the same

d) may increase or decrease

How does a Cyclotron work to accelerate electric charges to extremely high speeds ?

Helical Motion of a charged particle moving in a Magnetic field NOT perpendicular to its velocity. Discover the common misconceptions about the Helical path traced by particle.

a) A charged particle with charge q and mass m is projected with speed v in the positive x - direction. Magnetic field with magnitude B makes an angle q with the positive x - direction, as shown in figure. If the particle is required to hit point P at distance l on the line making an angle q with the positive x - direction, then what is the minimum value of magnetic field B required for it.

If initial velocity of a charged particle makes an angle (q) with the magnetic field, the particle follows a helical path.

a) If the initial speed is held fixed but angle q is changed, how does

Radius (r), Pitch (p) and Time period (T) vary with q.

b) What is the ratio of p/r for q = 30o, 45o, 60o

c) For what angle is p/r = 1, 2, 1/2.

A charged particle enters a region which offers a resistance against its motion and a uniform magnetic field exists in the region. The particle traces a spiral path as shown in figure. State whether the following statements are true or false.

a) Speed of particle decreases as it moves inward

b) Net force on the particle is always perpendicular to its velocity

c) Net force on the particle decreases as it moves inward

d) Angular speed of particle remains constant

e) There is no component of magnetic field in the plane of spiral

Net ElectroMagnetic force on a charged particle moving in an ElectroMagnetic Field.

A charged particle is released from rest in a region of uniform electric and magnetic fields which are parallel to each other. The particle will move in a a) straight line b) circle c) helix d) cycloid If the particle has an initial velocity parallel or anti-parallel to the fields,

the particle will move in a

a) straight line b) circle c) helix d) cycloid

Electric and Magnetic fields are present in space parallel to each other.

What is the path traced by the charged particle for the following cases of its velocity.

A particle of mass m and charge q is released from the origin in a region where electric field E and magnetic field B are present, perpendicular to each other, as shown in the figure. What is the path traced by the particle.

A positive and a negative charge is subjected simulteaneously to an electric field along the + x direction and a magnetic field along the +z direction, then

a) positive charge deflect towards +y direction and negative charge towards

-y direction

b) positive charge deflects towards -y direction and negative charge towards

-y direction

c) both deflect towards +y direction

d) both deflect towards -y direction

A charged particle is moving through a region of space. E and B represent the electric and magnetic fields respectively. (Ignore gravity)

If the particle moves undeflected, then this region of space may have

a) E = 0, B = 0

b) E = 0, B ? 0

c) E ? 0, B = 0

d) E ? 0, B ? 0

Repeat the above question, if the particle moves unaccelerated.

Repeat the above questions, including gravity.

Find the path traced by a charged particle for each of the case below.

Magnetic Force on a current carrying wire.

A wire of length l and mass m is suspended by a pair of flexible wires in a magnetic field with intensity B. What are the magnitude and direction of the current so that the tension in the wires is zero?

A wire of mass m lies perpendicularly on a pair of rails as shown in fig. A vertically downward magnetic field of strength B exists in the space. The rails are smooth but the coefficient of friction between the wire and the floor is m. A current i is established in the wires at t = 0.

a) Discuss the motion of the wire on the rails and floor.

b) How far from the rails will the wire reach?

If the rails were rough, such that the friction coefficient between the rails and the wire is m,

c) What should be the minimum value of m which can prevent the wire from sliding on the rails?

d) Describe the motion of the wire if the value of m is half of the above value.

A straight current carrying wire of length L is placed in a uniform magnetic field of strength B, as shown in the figure.

What is the torque acting on the wire

a) wrt its center

b) wrt its edge

A wire is bent as shown in figure ( each side is of length l ). Current in the wire is i and it is placed in a uniform magnetic field B.

Net force experienced by the wire is ......... in ........ direction.

A semi-circular wire of radius R and carrying current i is placed in a uniform magnetic field B perpendular to the plane of wire as shown in the figure.

a) What is the net force on the wire ?

b) What is the torque acting on the wire wrt point C ? point P ?

A semi-circular wire of radius R and carrying current i is placed in a uniform magnetic field B ib the plane of wire as shown in the figure.

a) What is the net force on the wire ?

b) What is the torque acting on the wire wrt point C ?

Toque due to Magnetic force on a current carrying loop placed in Magnetic field. Does the torque depend on the shape of loop ?

A wooden block of mass m is wrapped by a wire loop, carrying current i, as shown in the figure. The whole system is placed on a frictionless horizontal surface in a uniform magnetic field as shown in fig.

Find the distance of action of normal reaction from the center of mass as a function of current in the loop.

For what value of current does the block topple ?

How does a DC Motor work ?

Working of a Moving Coil Galvanometer to measure the electric current.

In a moving coil galvanometer, we use a radial magnetic field so that the galvanometer scale is a) logarithmic b) exponential

c) linear d) none of the above

The coil of a galvanometer is 10 cm 5 cm. It consists of 20 turns of the wire and is in a magnetic field of 0.1 T. The restoring torque constant of suspension fiber is 10-5 Nm/degree. Assuming magnetic field to be radial

a) What is the maximum current that can be measured by this galvanometer if scale can accommodate 90o deflection?

b) What is the smallest current that can be detected if minimum observed deflection is 0.1o ?

c) What is the current sensitivity of galvanometer ?

Is a current carrying loop like a Magnet ? Does a current carrying loop placed in a Magnetic field act like a Magnetic Dipole ?

A circular loop of radius R and carrying current i is placed in a uniform magnetic field B as shown in the figure.

What is the Magnetic moment of loop ?

What is the Torque acting on the loop ?

Does torque due to magnetic force on a current loop depend on the point of reference ?

Find the magnetic dipole moment of the loop shown in figure.

If the magnetic field exists in space as shown in figure, what is the torque acting on the loop ?

What is the net magnetic force acting on the loop ?

If the loops carry a current i, find their magnetic moments.

If magnetic field B k exists in the region, what is the torque acting on the loops ? What is the net magnetic force on the loops ?

A current carrying loop is placed in a uniform magnetic field in four different orientations, I, II, III and IV, arrange them in

a) increasing order of potential energy

b) increasing order of magnitude of torque acting on them

Figure shows one quarter of a circular loop of radius R that carries a current i. A uniform magnetic field B is directed as shown.

a) Find the magnetic moment of the coil.

b) In what direction does the loop tend to rotate ?

c) Find the torque acting on the coil.

d) What is the maximum torque on the coil ? e) What is the Potential Energy of coil in the position where torque is maximum

f) Find the potential energy of the coil in the given position

g) What is the work needed to rotate the loop from its position of minimum energy to the given orientation.

h) What is the work needed to rotate the loop from the given orientation to its position of maximum energy.

Are revolving charges like current loops ? Do revolving charge behave like Magnetic Dipoles ? What is Gyromagnetic Ratio ? Are Magnetic Moment and Angular Momentum of a rotating charged body related ?

A uniform rod and sphere have a total charge Q uniformly distributed over them. If they rotate with angular velocity w about the axis shown in the figures, find their magnetic moments.

A non-conducting disk of mass M and radius R rotates with an angular velocity w about its axis. Find the ratio of magnetic dipole moment and angular momentum, if a) both charge and mass are distributed uniformly over the surface of disk b) both surface charge density and mass density of disk is proportional to r c) surface charge density is proportional to r, but mass is distributed uniformly.

A charged particle + q of mass m is placed at a distance d from another charged particle -q of mass m in a uniform magnetic field B.

If the particles are projected towards each other with same speed v,

a) what is the maximum value of v for which the particles do not collide ?

b) if speed of particles if double of the maximum value of v calculated in part (a), what is the time after which the particles collide ?

c) if the particles undergo an in-elastic collision, what is the velocity and path traced by the combined particle after collision.

d) Repeat the above question if the charge and mass of second particle is

-3q and 3m instead of -q and m.

Two identical particles, separated by a distance d, are moving with speeds v1 and v2 as shown in fig. A uniform magnetic field B is present in the region, directed perpendicular to screen and inwards.

Find the condition for the particles to collide.

If the particles collide in-elastically, find the radius of combined particle after collision.

A positive charge moving with a velocity v enters the magnetic field at x = a.

The trajectory of the charge in this region can be like

A particle of mass m and charge q is projected into a region having a uniform magnetic field B of width d, perpendicular to the velocity, as shown in the figure.a) Find the angle of deviation q of the particle as it comes out of the magnetic field.

b) What is the distance travelled by the particle in the region of field ?

c) What is the time spent by the particle in the region of field ?

d) What should be the minimum value of d for which the particle turns back ?

The region with width L is filled with uniform steady magnetic field B (out of screen). A particle of mass m, positive charge q and velocity v enters the region of the magnetic field. Neglect gravity.

a) Find the value of L if the particle emerges from the region of magnetic field with its final velocity at an angle 30o to its initial velocity. Find the distance travelled by the particle and time spent in the field.

b) If the magnetic field now expands upto 2.1 L, find the distance travelled by the particle and time spent in the field

A proton and an alpha particle are projected in a magnetic field which exists in a region of width d. Compare the

a) radius of circular path

b) angle of deviation from initial velocity

c) distance travelled by the particle in the region of field

d) time spent by the particle in the region of field if before entering the magnetic field, both the particles

a) have the same speed

b) have the same momentum

c) have the same kinetic energy Take ma = 4mp, qa = 2qp

A particle of mass m and charge q moving with speed v, enters a region of uniform magnetic field of strength B as shown in figure.

a) Find the length of straight line between the point of exit and point of entry. What is the time spent by the particle in the region of field.

b) Repeat the above question, if the direction of field is reversed.

A small charge ball having mass m and charge q is suspended from a rigid support by means of an inextensible thread of length l. it is made to rotate on a horizontal circular path in a uniform, time independent magnet field of induction B which is directed downwards. The time period of revolution of the ball is To. If the thread is always stretched, calculate the radius of circular path on which the ball moves.

A particle of charge q and mass m is projected towards a circular region having uniform magnetic field B perpendicular and out of the plane of paper as shown in fig. If the line OP makes an angle q with the direction of initial velocity then find the initial speed so that particle passes through point O.

A uniform magnetic field exists in a region which forms an equilateral triangle of side a. The magnetic field is perpendicular to the plane of the triangle. A charge q enters into this magnetic field perpendicular to a side with speed v. Find the speed of particle so that the charge enters and leaves the field from midpoint of either side.

A block of mass m and carrying a charge q is attached to a spring with spring constant k. It is executing SHM on a horizontal frictionless surface. If Magnetic field B is present in space as shown in the figure, what is the maximum amplitude of oscillation, for which the block can execute SHM.

A positive and a negative charge is subjected simulteaneously to an electric field along the + x direction and a magnetic field along the +z direction, then

a) positive charge deflect towards +y direction and negative charge towards

-y direction

b) positive charge deflects towards -y direction and negative charge towards

-y direction

c) both deflect towards +y direction

d) both deflect towards -y direction

A particle of charge +q and mass m moving under the influence of a uniform electric field E i and uniform magnetic field B k follows a trajectory from Q to R as shown in figure. Which of the following statement(s) is / are correct?

A particle of mass 10-26 kg and charge + 1.6 10-19 C travelling with a velocity 1.28 106 m/s in the +x direction enters a region in which a uniform electric field Ey = 102.4 kV/m and a uniform magnetic field Bz = 8 10-2 T are present. The particle enters this region at the origin at time t = 0.

Determine the location of the particle at t = 5 10-6 s.

If the electric field is switched off at this instant (with the magnetic field still present), what will be the position of the particle at t = 7.5 10-6 s ?

A positively charged particle, having charge q and mass m, is moving along the x-axis with speed v. It enters a region where an electric field E exists. The direction of the electric field is along positive y-axis and it exists in the region bounded by the lines x = 0 and x = l.

Find the time taken by the particle to cross the region of Electric Field. Just at the moment the particle is about to leave the region of Electric field, Electric field is switched Off and Magnetic Field B, directed along positive y-axis, is switched On.

What is the radius and pitch of the helix ? If the strength of electric was double, how would the radius and pitch be affected ?

Electric and Magnetic fields are present in space such that they are parallel to each other. A rough plane ( with coefficient of friction = m ) is present such that both the fields are perpendicular to the plane as shown.

A charged particle, with charge q and mass m, is projected on the plane with speed vo.

a) What is the nature of path traced by the particle.

b) What is the time taken by the particle to stop.

c) What is the total distance travelled by the particle on the plane..

A positively charged particle is moving initially along the x-axis. There is a sudden change in the path due to the presence of electric and/or magnetic fields. The curved path followed by the particle is in the x - y plane and is found to be non-circular.

Which of the following combinations is possible ?

A charged particle of specific charge (charge/mass) a is released from origin at time t = 0 with velocity v = vo ( i + j + k ) in uniform magnetic field B = B i Coordinates of the particle at time t = p / (Ba) are

A particle of mass m and charge q is moving in a region where uniform, constant electric and magnetic fields E and B are present. E and B are parallel to each other. At time t = 0, the velocity vo of the particle is perpendicular to E.

a) Find the velocity v of the particle at time t. You must express your answer in terms of t, q, m, the vector vo, E and B and their magnitudes vo, E and B.

b) Find the time at which speed of particle becomes double of the initial speed

c) At what coordinate y, does the particle cross the y-axis for nth time ? What is the angle between the velocity vector of particle and y-axis at this moment.

A semicircular wire of radius R, carrying current i, is placed in a magnetic field as shown in figure.

i) The magnetic force experienced by the wire would be a) 2iBoR b) 3iBoR c) 5 iBoR d) 10 iBoR

ii) Net torque on the wire wrt point C will be _______ ?

In figure, a three sides frame is pivoted about its upper horizontal sections and hangs vertically. Its sides are each of the same length l and have a linear density l. A current i is sent through the frame, which is in a uniform magnetic field B directed upward.

Through what angle will the frame be deflected?

A square loop of uniform conducting wire is as shown in figure. A current i (in amperes) enters the loop from one end and exits the loop from opposite end as shown. The length of each side of the square loop is l meters but the resistance of each side is not equal. The loop is subjected to different magnetic fields.

What is the magnetic force on the loop in each case ?

Consider the frames shown in figure. Resistance of each section of frame is different and distribution of current in each section is not known.

Find the net magnetic force on each frame.

A metal rod of mass m and length l, is placed on a set of rough metal rails as shown in the figure. If coefficient of friction between the rod and rails is m,

what is the range of current in the rod for which it can stay in equilibrium ?

If the rails were frictionless, for what current will the rod be in equilibrium ?

A conducting ring of mass m and radius r has a weightless conducting rod PQ of length 2r and resistance 2R attached to it along its diameter. It is pivoted at its centre O. Two blocks of mass m and 2m are suspended by means of a light inextensible string passing over it as shown in figure. System is placed in a magnetic field B (into the plane of the ring). A circuit is now completed by connecting the ring at N and O to a battery of emf V. For what value of V, will the system remain static.

A rod of mass m kg and radius r meters rests on two parallel rails that are distance d meters apart. The rod carries a current of i A (the direction of current can be inferred from the figure) and rolls over the rails without slipping. A uniform magnetic field of magnitude B Tesla is directed perpendicular to the rod and the rails. If it starts from rest, what is the speed of the rod as it leaves the rails.

A conducting circular loop of radius R carries a current i. It is placed in a uniform magnetic field B such that B is perpendicular to the plane of the loop. The magnetic force acting on the loop causes the loop to

a) contract b) expand

c) either contract or expand d) cannot be determined

If R = 10 cm and B = 10 T, and tensile strength of the wire is equal to T = 10 N. Find i ( in Amp ) at which the ring is broken.

A current carrying loop is placed in the non-uniform magnetic field whose variation in space is shown in figure. Direction of magnetic field is into the plane of screen. The magnetic force experienced by the loop is

a) non zero b) zero

c) cannot say anything d) none of the above

A strong magnet is placed under a horizontal conducting ring of radius R that carries current i as shown in figure. If the magnetic field makes an angle q with the verticle at the rings location,

What is the magnitude and direction of resultant force on the ring ?

For what value of current can the ring balance its weight ?

A current loop is placed in a non-uniform magnetic field as shown in fig. Is the net force on the loop zero ? Is the net torque on the loop zero ? Repeat the above question if the loop is rotated by 90o about z-axis or y-axis.

A uniform tube of square cross-section with side a is filled with a conducting fluid. Current i is passed between the electrodes marked in the figure. Magnetic field B is also present in the space.

What will be difference in the levels of fluid in equilibrium

(given: r = density of fluid)

A moving coil galvanometer experiences torque = k i, where i is current. If the coil has moment of inertia I and N turns of area A each, and is kept in magnetic field B

a) Find k in terms of given parameters.

b) If for current i deflection is p/2, what is the torsional constant of spring

c) If a charge Q is passed suddenly through the galvanometer, what is the maximum angle of deflection

A ring of radius R having uniformly distributed charge Q is mounted on a rod suspended by two identical strings. Initial tension in strings is To. Now a vertical magnetic field is switched on and ring is rotated at constant angular velocity w. Find the maximum w with which the ring can be rotated if the strings can withstand a maximum tension of 3To/2.

Find the magnetic dipole moment of the loop shown in the figure.

If a magnetic field with magnitude B is present along z direction, what is the torque acting on the loop ?

What is the net magnetic force on the loop ?

A small circular coil with mass of M and radius R, carries a current i. The coil is located in a uniform magnetic field B with magnetic moment of coil originally parallel to the field direction.

a) If the loop is displaced by a small angle q (such that its magnetic moment makes an angle with the field), what is the angular frequency of oscillations of the coil.

b) What will be its angular speed when it passes through equilibrium position ? Assume friction to be absent.

A current carrying loop lies on a smooth horizontal plane. Then,

a) is it possible to establish a uniform magnetic field in the region so that the loop starts rotating about its own axis ?

b) is it possible to establish a uniform magnetic field in the region so that the loop will tip over about any of the point ?

c) what is the maximum value of current for which the loop will not tip over

d) If the loop is hung, as shown in the figure, for what value of current can the loop stay in horizontal position.

A uniform constant magnetic field B is directed at an angle of 45o to the x-axis in x-y plane. A rigid square wire frame carrying a steady current i is placed in the field with its center at the origin. At time t = 0, the frame is at rest in the position shown in the figure with its sides parallel to x and y-axes. Each side of the frame is of mass M and length L.

What is the angular acceleration of loop at this moment.

What is the angular displacement of loop in a small time interval Dt

A rectangular loop PQRS made from a uniform wire has length a, width b and mass m. It is free to rotate about the arm PQ, which remains hinged along the horizontal line taken as the y-axis. A uniform magnetic field B = ( 3i + 4k ) B exists in the region. The loop is held in the x - y plane and a current i is passed through it. The loop is now released and is found to stay in the horizontal position in equilibrium.

Find the magnetic moment of a half tore. Current in the wire is i, radius of cross-section of tore is R and the number of turns of wire is N.

In figure, a coil of single turn, carrying a current i, is wound on a sphere of radius R and mass m. The plane of the coil is parallel to the inclined plane and lies in the equatorial plane of the sphere. If the sphere is in rotational equilibrium, the value of B is If the surface is made frictionless, find the initial angular acceleration of the sphere

a) wrt the center of mass of sphere

b) wrt the point of contact

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