FREQUENTLY ASKED QUESTIONS FOR REVISION CHAPTER:4 MAGNETIC EFFECT OF CURRENT ONE MARK QUESTIONS 1 Write the expression in a vector form for the Lorentz magnetic force F due to a 2013 charge moving with a velocity V in a magnetic field B .What is the direction fo the magnetic force 2 What is the direction of the force acting on a charge particle q, moving with a 2008 velocity vin a uniform magnetic field B? 3 An electron does not suffer any deflection while passing through a region of 2009 uniform magnetic field. What is the direction of the magnetic field? 4 A beam of particles projected along +x-axis, experiences a force due to a 2012 magnetic field along 2007 the +y-axis. What is the direction of the magnetic field?
5 Write two factors by which voltage sensitivity of a galvanometer can be increased. 2008 6 Write two properties of a material used as a suspension wire in a moving coil 2006 galvanometer. 7 An electron moving through a magnetic field does not experience a force; under 2005 what condition is it possible? 8 Name the physical quantity whose S I unit is Wb-m2, is it ascalar or vector quantity? 2005 9 Two wires of equal length are bent in the form of two loops , One of the loops is 2005 square shaped and another is circular. These loops are suspended in a uniform magnetic field and same current is passed through them. Which loop will experience greater torque? 10 How does the magnetic moment of an electron in a circular orbit of radius ‘r’ and 2005 moving with a speed ‘v’ change ,when the frequency of revolution doubled? c
TWO MARKS QUESTIONS 1 201 5 A square loop of side 20 cm carrying current 1 A is kept near an infinitely long straight wire carrying current 2 A ,calculate the magnitude and direction of net force on the loop due to the current carrying con doctor. 2 A square shaped plane coil of area 100 cm2 of 200 turns caries a steady current of 5 201 A . it is placed in a uniform magnetic field of 0.2 T acting perpendicular to the plane 4 of the coil. Calculate the torque on the coil when its plane makes an angle of 60o with the direction of the field. In which orientation will the coil be in stable equilibrium? 3 An ammeter of resistance 0.80 can measure current upto 1.0 A. 201 (i) What must be the value of shunt resistance to enable the ammeter to measure 3 current upto 5.0 A? 200 (ii) What is the combined resistance of the ammeter and the shunt? 7 4 Two identical circular wires P and Q each of radius R and carrying current ‘I’ are 201 kept in perpendicular planes such that they have a common centre as shown in the 2 figure. Find the magnitude and direction of the net magnetic field at the common centre of the two coils.
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Two identical circular loops, P and Q, each of radius r and carrying currents I and 2I respectively are lying in parallel planes such that they have a common axis. The direction of current in both the loops is clockwise as seen from O which is equidistant from the both loops. Find the magnitude of the net magnetic field at point O. 5 A wire of length L is bent round in the form of a coil having N turns of same radius. If a 2009 steady current I flows through it in a clockwise direction, find the magnitude and direction of the magnetic field produced at its centre 6 A straight wire carrying a current of 12 A is bent into a semi-circular arc of radius 201 0
20 cm as shown. What is the magnetic field B at O due to (i) straight segments (ii) the semi-circular arc? 7 A jet plane is travelling west at 450 ms 1. If the horizontal component of earth’s 200 magnetic field atthat place is 4 104tesla and the angle of dip is 30°, find the emf 8 induced between the ends ofwings having a span of 30 m. 8 Write the expression for Lorentz magnetic force on a particle of charge ‘q’ moving 201 with velocity v in a magnetic field B . Show that no work is done by this force on the 2 charged particle. 9 A steady current (I1) flows through a long straight wire. Another wire carrying steady 201 current (I2) in the same direction is kept close and parallel to the first wire. Show with 2 the help of a diagram, how the magnetic field due to the current I1 exerts a magnetic force on the second wire. Write the expression for this force.
10 A rectangular loop of wire of size 4 cm × 10 cm carries a steady current of 2A. A 201 straight long wire carrying 5A current is kept near the loop as shown. If the loop and 2 the wire are coplanar, find (i) the torque acting on the loop and (ii) The magnitude and direction of the force on the loop due to the current carrying wire.
11 A particle of charge ‘q’ and mass ‘m’ is moving with velocity V. It is subjected to a uniform magnetic field B directed perpendicular to its velocity. Show that it describes a circular path. Write the expression for its radius THREE MARKS QUESTIONS 1 A closely wound solenoid of 2000 turns and cross sectional area 1.6 x10–4m2 carrying a 2014 current of 4.0 A is suspended through its centre allowing it to turn in a horizontal plane. Find the magnetic moment associated with the solenoid, (ii) Magnitude and direction of the torque on the solenoid if a horizontal magnetic field of 7.5x10–2T is set up at an angle of 30with the axis of the solenoid.
2 State the principle of working of a galvanometer. A galvanometer of resistance G is 2015 converted into a voltmeter to measure upto V volts by connecting a resistance R1 in series with the coil. If a resistance R2 is connected in series with it, then it can measure upto V/2 volts. Find the resistance, in terms of R1 and R2, required to be connected to convert it into a voltmeter that can read upto 2 V. Also find the resistance G of the galvanometer in terms of R1 and R2.
3 (a) Why is the magnetic field radial in a moving coil galvanometer? Explain how it is 2013 achieved. (b) A galvanometer of resistance ‘G’ can be converted into a voltmeter of range (0-V) volts by connecting a resistance ‘R’ in series with it. How much resistance will be required to change its range from 0 to V/2?
4 Deduce the expression for the torque acting on a planar loop of area A and carrying 2010 current I placed in a uniform magnetic field B, If the loop is free to rotate, what would be its orientation in stable equilibrium?
5 A cyclotron’s oscillator frequency is 10 MHz. What should be the operating magnetic field 2006 for accelerating protons? If the radius of its ‘dees’ is 60 cm, calculate the kinetic energy (in MeV) of the proton beam produced by the accelerator.
6 State Biot – Savart law. Deduce the expression for the magnetic field at a point on the axis of 2007 a current carrying circular loop of radius ‘R’, distant ‘x’ from the centre. Hence write the magnetic field at the centre of a loop. 7 A uniform magnetic field of 6·5 10– 4 T is maintained in a chamber. An electron enters into 2008 the field with a speed of 4·8 106 m/s normal to the field. Explain why the path of the 2011 electron is a circle. Determine its frequency of revolution in the circular orbit. Does the frequency depend on the speed of the electron ? Explain. 8 A uniform magnetic field is set up along the positive x-axis. A particle of charge ‘q’ and 2013 mass ‘m’ moving with a velocity v enters the field at the origin in X-Y plane such that it has velocity components both along and perpendicular to the magnetic field B Trace, giving reason, the trajectory followed by the particle. Find out the expression for the distance moved by the particle along the magnetic field in one rotation. 9 A wire AB is carrying a steady current of 12 A and is lying on the table. Another wire CD carrying 5A 2010 is held directly above AB at a height of 1 mm. Find the mass per unit length of the wire CD so that it remains suspended at its position when left free. Give the direction of the current flowing in CD with respect to that in AB. [Take the value of g = 10 ms–2] 1 Depict the field-line pattern due to a current carrying solenoid of finite length. 2009 0 (i) In what way do these lines differ from those due to an electric dipole? (ii) Why can’t two magnetic field lines intersect each other? 1 A long straight wire AB carries a current I. A proton P travels with a speed v, parallel to the wire, at a 2010 1 distance d from it in a direction opposite to the current as shown in the figure. What is the force experienced by the proton and what is its direction?
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An -particle and a proton moving with the same speed enter the same magnetic field region at right angles to the direction of the field. Show the trajectories followed by the two particles in the region of the magnetic field. Find the ratio of the radii of the circular paths which the two particles may describe.
FOUR MARKS (VALUE BASED QUESTIONS) 1 Asha’s uncle was advised by his doctor to have an MRI (magnetic resonance imaging) 201 scan of his brain. Her uncle felt that it was too expensive and wanted to postpone it. When 5 Asha learnt about this, she took the help of her family and when she approached the doctor, he also offered a substantial discount. She thus convinced her uncle to undergo the test to enable the doctor to know the condition of his brain. The resulting information greatly helped his doctor to treat him properly. Based on the above paragraph, answer the following questions : (a) What according to you are the values displayed by Asha, her family and the doctor ? (b) What in your view could be the reason for MRI test to be so expensive? (c) Assuming that MRI test was performed using a magnetic field of 0·1 T, find the maximum and minimum values of the force that the magnetic field could exert on a proton (charge = 1·6 x 10–19C) that was moving with a speed of 104 m/s. 2 Deepika and Ruchika were asked by their teacher to perform an experiment using a 201 galvanometer. Before doing the experiment they were very keen to know the different parts 4 of the galvanometer which was given to them in the form of a small box. They approached the teacher and asked for the permission. The teacher thought it would be a good idea if the galvanometer be opened before the whole class and explained its construction and working to all of them. Based on the above paragraph, answer the following questions : (a) What, in your opinion, were the qualities displayed by Deepika, Ruchika and the teacher? (b) State briefly the working principle of the galvanometer. (c) What is the shape of the magnets used and why is it so designed?
FIVE MARKS QUESTIONS 1 (a) Use Biot-Savart law to derive the expression for the magnetic field due to a 201 circular coil of radius R having N turns at a point on the axis at a distance ‘x’ from its 0 centre. Draw the magnetic field lines due to this coil. 201 (b) A current ‘I’ enters a uniform circular loop of radius ‘R’ at point M and flows out 5 at N as shown in the figure. Obtain the net magnetic field at the centre of the loop.
2 (a) Show how Biot-Savart law can be alternatively expressed in the form of 200 Ampere’s circuital law. Use this law to obtain the expression for the magnetic field 3 inside a solenoid of length ‘l’, cross-sectional area ‘A’ having ‘N’ closely wound turns and carrying a steady current ‘I’. Draw the magnetic field lines of a finite solenoid carrying current I. (b) A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in therod through the wires. Find the magnitude and direction of the magnetic field which should be set up in order that the tension in the wire is zero.
3 (a) State Ampere’s circuital law. Use this law to obtain the expression for the 200 magnetic field inside an air cored toroid of average radius ‘r’, having ‘n’ turns per 8 unit length and carrying a steady current I. 200 (b) An observer to the left of a solenoid of N turns each of cross section area ‘A’ 5 observes that a steady current I in it flows in the clockwise direction. Depict the magnetic field lines due to the solenoid specifying its polarity and show that it acts as a bar magnet of magnetic moment m = NIA. 4 (a) Draw the magnetic field lines due to a circular loop of area A carrying current I. 201 Show that it acts as a bar magnet of magnetic Moment m =AI . 3 (b) Derive the expression for the magnetic field due to a solenoid of length ‘2 l’, radius ‘a’ having ‘n’ number of turns per unit length and carrying a steady current ‘I’ at a point on the axial line, distant ‘r’ from the centre of the solenoid. How does this expression compare with the axial magnetic field due to a bar magnet of magnetic moment ‘m’? 5 (a) Draw a labelled diagram of a moving coil galvanometer. State its working 201 principle. What is the function of a cylindrical soft iron core used in it ? 4 (b) Define the terms (i) current sensitivity and (ii) voltage sensitivity. (c) Explain the underlying principle used in converting a galvanometer into a (i) voltmeter and (ii) ammeter. 6 Draw a schematic sketch of a cyclotron. Explain its working principle. Obtain the 201 necessary mathematical expression to show how this machine is used to accelerate 1 charged particles 7 (a) State Ampere’s circuital law. Show that the magnetic field B at a distance r 201 outside the straight infinite wire carrying current I is tangential and is given by 4 B = µo I / (2πr). (b) Consider a long straight cylindrical wire of circular cross-section of radius a, as shown in the figure. The current I is uniformly distributed across this cross-section. Calculate the magnetic field B in the region r < a and r > a. Plot a graph of B versus r from the centre of the wire.
8 Two infinitely long straight parallel wires, ‘1’ and ‘2’, carrying steady currents I1 and I2 201 in the same direction are separated by a distance d. Obtain the expression for the 1 magnetic field due to the wire ‘1’ acting on wire ‘2’. Hence find out, with the help of a suitable diagram, the magnitude and direction of this force per unit length on wire ‘2’ due to wire ‘1’. How does the nature of this force change if the currents are in opposite direction? Use this expression to define the S.I. unit of current
9 Explain, using a labelled diagram, the principle and working of a moving coil 200 galvanometer. What is the function of (i) uniform radial magnetic field, (ii) soft iron 4 core? 201 Define the terms (i) current sensitivity and (ii) voltage sensitivity of a galvanometer. 2 Why does increasing the current sensitivity not necessarily increase voltage sensitivity?
10 a) Derive the expression for the torque on a rectangular current carrying loop 200 suspended in a uniform magnetic field. 8 b) A proton and a deuteron having equal momentum enter in a region of uniform magnetic field at right angle to the direction of the field. Depict their trajectories in the field.
11 (a) Using Biot-Savart’s law, derive an expression for the magnetic field at the centre 200 of a circular coil of radius R,number of turns N, carrying current I. 9 (b) Two small identical circular coils marked 1 and 2 carry equal currents and are placed with their geometric axes perpendicular to each other as shown in the figure. Derive an expression for the resultant magnetic field at O.
12 If a particle of charge q is moving with velocity v along the y-axis and the magnetic field B is 200 acting along the z-axis, use the expression Fq ( v B) to find the direction of the 9 force F acting on it. A beam of proton passes undeflected with a horizontal velocity v, through a region of electric and magnetic fields, mutually perpendicular to each other and perpendicular to the direction of the beam. If the magnitudes of the electric and magnetic fields are 100 kV/m, 50 mT respectively, Calculate (i) velocity of the beam (ii) Force exerted by the beam on a target on the screen, if the proton beam carries a current of 080 mA.
13 Explain the principle and working of a cyclotron with the help of a schematic 200 diagram. Write 7 the expression for cyclotron frequency. 201 0 14 If a particle of charge q is moving with velocity v along the y-axis and the magnetic 200 field B isacting along the z-axis, use the expression 8 F q ( v x B) to find the direction of the force F acting on it. A beam of proton passes undeflected with a horizontal velocity v, through a region of electric andmagnetic fields, mutually perpendicular to each other and perpendicular to the direction of thebeam. If the magnitudes of the electric and magnetic fields are 100 kV/m, 50 mT respectively,calculate (i) Velocity of the beam v. (ii) force exerted by the beam on a target on the screen, if the proton beam carries a current of 080 mA 15 (a) State the principle of the working of a moving coil galvanometer, giving its 201 labelled diagram. 1 (b) “Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity.” Justify this statement. (c) Outline the necessary steps to convert a galvanometer of resistance RG into an ammeter of a given range. 16 a) Using Ampere’s circuital law, obtain the expression for the magnetic field due to a 201 long 1 Solenoid at a point inside the solenoid on its axis. (b) In what respect is a toroid different from a solenoid? Draw and compare the pattern of the magnetic field lines in the two cases. (c) How is the magnetic field inside a given solenoid made strong?
EXPECTED QUESTIONS FOR REVISION/MLL CHAPTER:5 MAGNETISM 1 Write the magnetic properties of materials used preparing I. permanent magnets II. electromagnets III. Core of the transformer Give one example each.
2 The horizontal component of the earth’s magnetic field is equal to the vertical component at a place. Find the angle of dip?
3 Define the three elements to describe Earth’s magnetism at a place,show them in a diagram.
4 A uniform magnetic field gets modified as shown below when two specimens X and Y are placed in it. Identify whether specimens X and Y are diamagnetic, paramagnetic or ferromagnetic.
5 Which of the following substances are diamagnetic? Bi, Al, Na, Cu, Ca and Ni
6 How does angle of dip change as one goes from magnetic pole to magnetic equator of the Earth?
7 The permeability of a magnetic material is 0.9983. Name the type of magnetic materials it represents. 8 The susceptibility of a magnetic material is 1.9 × 10–5. Name the type of magnetic materials it represents. 9 The susceptibility of a magnetic materials is –4.2 × 10 6 . Name the type of magnetic materials it represents.
1 In what way is Gauss’s law in magnetism different from that used in electrostatics? Explain briefly. 0 The Earth’s magnetic field at the Equator is approximately 0.4 G; Estimate the Earth’s magnetic dipole moment. Given: Radius of the Earth = 6400 km.
1 How the following magnetic materials behave with the rise of temperature 1 Para,Ferro,Dia-magnetic substances 1 Distinguish between Para, Ferro Dia-magnetic substances, give one example each 2 1 Deduce the expression for magnetic dipole moment of an electron revolving around the 3 Nucleus in a circular orbit of radius ‘r’. Indicate the direction of the magnetic dipole moment.
1 Deduce the expression for magnetic field due to a magnetic dipole at any point on the 4 I. Axial line II. Equatorial line Describe the expression for torque experienced by a dipole in a uniform magnetic field.
1 How magnetic field lines are different from electric field lines? Write any two properties of 5 magnetic field lines. 1 Define the terms 6 I. Magnetic permeability II. Retentively III. Coercively IV. Susceptibility What do the area of the Hysteresis loop and slope of the graph between I and H signify?