Download MAGNETIC EFFECTS OF CURRENT & MAGNETISM (Important formulae & concepts)

MAGNETIC EFFECTS OF CURRENT & MAGNETISM
(Important formulae & concepts)
II. MOTION OF CHARGED PARTICLES IN
ELECTRIC AND MAGNETIC FIELDS
QUESTIONS FOR
SLOW & AVERAGE STUDENTS
1. The force F experienced by a particle of charge of moving with a velocity v in a magnetic field
B is given by F = q (v x B ). Which pair of vectors is always right angle to each other?
2. Why does the energy of a moving charge particle in a uniform magnetic field does not change?
[Hint : The magnetic force acts perpendicular to the direction of motion, there is no change in the
speed so kinetic energy remains constant.]
3. How does the deflection produced on a moving proton by electric ad magnetic field differ?
4. A galvanometer gives full scale deflection for a current ig, can it be converted into an ammeter
whose range is i< ig? [Hint: Shunt required S= igG/(i-ig); as i <ig shunt will be negative which is
not possible.]
5. Why is magnetic field in a moving coil galvanometer made radial?
6. Why does Earth’s magnetic field not affect a moving coil galvanometer? [Hint : Earth’s magnetic
field is very weak as compared to the magnetic field in moving coil galvanometer.]
7. Why do we use phosphor bronze as a suspension fibre in a moving coil galvanometer?
8. Can a cyclotron be used to accelerate neutrons, give reason for your answer?
9. An irregular loop carrying current is located in an external magnetic field, what shape does it
acquire if the wire is flexible and why? [Hint : Circular, so that maximum magnetic flux passes
through it, for a given perimeter area of a circle is maximum.]
10. A current carrying loop in a magnetic field is not rotating, under what circumstances it is
possible? [Hint: When the plane of the loop is perpendicular to magnetic field.]
11. Give reason why tow wires carrying current in the same direction attract each other where as
two because of electrons traveling in the same direction repel each other.
12. A proton and an -particle enter a uniform magnetic field perpendicularly, with the same speed.
How many times is the ti,e period of the -particle than that of the proton? Deduce an
expression for the ratio of the radii of the circular paths of the two particles.
[Hint :
T = 2m/qB
Tp = 2m/qB
T = [2(4m)]/B (2q) = 2Tp
r = mv/(qB) or
r  m/q
rp/ ra = [mp/m] x [q/qp] = ¼ x 2/1 = ½
13. To increase the current sensitivity of a moving coil galvanometer by 50%, its resistance is
increased so that the new resistance becomes twice its initial resistance. By what factor does its
voltage sensitivity change?
[Hint : Current sensitivity is = NBA/k
Voltage sensitivity
Vs’ = NBA/KR = Is/R
New current sensitivity
is’ = is + (50/100)Is = (3/2) is
New voltage sensitivity
Vs’ = (3/2)is/2R = (¾) (is/R) = (¾) Vs
The voltage sensitivity reduces by 25%
14. An electron is circulating in a plane right angle to a uniform magnetic field B= 1x10 -4 tesla. What
is its orbital radius? (Give V=1.9x106 ms-1)
15. An electron emitted by a heated cathode and accelerated through a potential difference of 2.0
kV, enters a region with uniform magnetic field of 0.15 T. Determine the trajectory of the electron
if the field (i) is transverse to its initial velocity, (ii) makes an angle of 30 o with the initial velocity.
16. Two straight wires A and B of length 10 m and 12 m carrying currents of 4.0 A and 6.0 A
respectively in opposite directions lie parallel to each other at a distance of 3.0 cm. estimate the
force on a 15 cm section of the wire B near its centre.
17. A proton enter the magnetic field of flux density 3T with a velocity 5x10 6 m/s at an angle 30o
with field. Find the magnitude of force on proton.
18. A -particle is moving with a speed of 9x105 m/s at right angles to a magnetic field of flux density
3 Wb/m2. What is the acceleration of  particles?
m = 6.65x10-27 kg
q = 3.2 x10-19c
19. A long straight conductor carries a current 2.5A. A electron travels with a velocity 5x10 5 m/s
parallel to the wire 0.2m away from it and in the direction opposite to the current. What force
does the magnetic field of current exert on the electron?
20. A 3cm wire carrying a current of 10A is placed inside a solenoid perpendicular to its axis. The
magnetic field inside the solenoid is given to be 0.27T. What is magnetic force on the wire?
21. Why the earth’s magnetic field does not effect the working of a moving coil galvanometer.
22. Why the high resistance in series is connected to make a voltmeter, where as a low resistance in
parallel is connected to make an ammeter?
23. The coil of a galvanometer is 0.02 x 0.08m2. It consists of 200 turns of fine wire and is in a
magnetic field of 0.2 T. The restoring torque constant of the suspension fibre is 10 -6 Nm per
degree. Assuming magnetic field to be radial. What is the maximum current that can be
measured by the galvanometer, if the scale can be accommodate 30 o deflection?
24. It is desired pars only 5% of current through a galvanometer of resistance 95. What shunt
resistance should be connected across it?
25. A voltmeter of resistance R1 is to be used to measure a voltage 100 times as large as it can
measure without an additional resistance in series. How large is the resistance to be used in series
with the meter?
26. On what very principle cyclotron works?
27. Can a charged particle accelerate in magnetic field only
28. Find the formula for cyclotron frequency.
29. Find the ratio of radii of -particle and proton if they are projected with equal velocity in the
magnetic field.
30. In a chamber, a uniform magnetic field of 6.5G (1 G= 10 -4T) is maintained. An electron is shot
into the field with a speed of
4.8x106 ms-1 normal to the fields. Explain why the path of the
electron is a circle. Determine the radius of the orbit.
31. Obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on
the speed of the electron? Explain.
32.Why should the spring/suspension wire in a moving coil galvanometer have a low
torsional constant.?
33. Using Ampere’s circuital law obtain an expression for the magnetic field along the axis of the
current carrying solenoid of length ‘l’and N number of turns.
34. A circular coil of 200 turns and radius 10cm is placed in the uniform magnetic field of 0.5 T
normal to the plane of the coil. If the current in the coil is 3A, calculate the
(i) total torque on the coil
(ii) total force on the coil
(iii) average force on each electron in the coil due to magnetic field (assume the area of cross
section of the wire to be 10-3m2 and the free electron density is 1029m-3)
35.A proton is moving along the positive x-axis in the presence of uniform magnetic field along
the positive y-axis. What is the direction of force acting on it.
(HOT,S) QUESTIONS FOR
BRIGHT STUDENTS
1. A current of 1A is flowing in the sides of an equilateral triangle of side 2m.Find the
magnetic field at the centroid of the triangle.
Ans.
It is clear that all the three sides of the triangle will produce magnetic field at the
centroid O in the same direction. Therefore, total magnetic field at O is = 3 × magnetic field due
to one side.
Magnetic field at O due to side BC is
2. A square loop of wire of side 2l carries a current I. What is the magnetic field at the centre
of the square? If the square wire is reshaped into a circle, would the magnetic field increase
or decrease at the centre?
Ans.
Figure (i) shows the conditions of the problem. It is clear that each side of the square produces
magnetic field at the centre O of the square in the same direction. Therefore, total magnetic field
at O = 4 × magnetic field due to one side. Magnetic field at O due to side AB is
3.A cell is connected across points A and B of a uniform circular conductor. Prove that the
magnetic field at its centre O will be zero
Ans. Figure shows the conditions of the problem. The two paths ADB and ACB are in parallel.
Let I1 and l1 be the current and length of path ADB; I2 and l2 being that for path ACB. If k is the
resistance per unit length,then,
By right-hand palm rule, the directions of B1 and B2 are opposite. Hence the resultant magnetic
field at O is zero.
4. The Fig. shows a right angled isosceles triangle PQR having its base equal to a. A current of I
amperes is passing downwards along a thin straight wire cutting the plane of the paper normally
as shown at Q. Likewise, a similar wire carries an equal current passing normally upwards at R.
Find the magnitude and direction of magnetic flux
density B at P. Assume the wires to be infinitely long
Ans:
5. An electron with a velocity of 3 × 107 ms–1 enters a uniform electric field at right angles to the
lines of force. If the field is produced by applying 500 V between two parallel plates 6 cm long
and 2 cm apart, at what angle will the electron leave the uniform electric field at the end of the
paralled plates? Assume e/m = 1.8 × 1011 C kg–1.
Ans.
6. An electron beam passes through a magnetic field of 2 × 10 –3 Wb / m2 and an electric field of
3.4 × 104 Vm–1, both acting simultaneously. If the path of the electron remains undeviated,
calculate the speed of the electrons. If the electric field is removed, what will be the radius of the
circular path? Mass of electron = 9.1 × 10–31 k.g.
Ans:
7. Two long horizontal wires are kept parallel at a distance of 0.2 cm apart in a vertical plane.
Both the wires have equal currents in the same direction. The lower wire has a mass of 0.05kg/m.
If the lower wire appears weightless, what is the current in each wire?
Ans: Let I amperes be the current in each wire. The lower wire is acted upon by two forces viz.
(i) upward magnetic force, and (ii) downward force due to weight of the wire. Since the lower
wire appears weightless, the two forces are equal over 1m length of the wire.
MAGNETISM
MAGNETIC MATERIALS
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EDITED BY
Mr. S.K.BHAT (VICE PRINCIPAL)
Mr. A.K.SHARMA (P.G.T..Physics)