1) An electron traavelling with a velocity 1



ANJUMAN COLLEGE OF ENGINEERING & TECHNOLOGY, NAGPUR

BE –Second Semester

ADVANCED PHYSICS

Unit-II - ELECTRON BALLISTICS

(Numerical)

1. A proton accelerates from rest in a uniform electric field of 500 N/C. At some

time later its speed is 2.5 x 106 m/s.

a) Find the acceleration of the proton.

b) How long does it take the proton to reach the above velocity?

c) How far has it moved in this time?

d) What is its kinetic energy at this time? (S-2014)

2. An electron starts from rests and moves freely in an electric field of intensity

1500 V/m . Determine the force on the electron and acceleration attained by the electron. (S-2008)

3 An electron traveling with initial velocity of 4 x 106 m/s enters a region of

uniform electric field of strength 2.5 x 104 N/C along the field lines.

a) Find the deceleration of the electron.

b) Determine the time taken by the electron to come to rest after it enters the field.

c) How far does the electron move in the electric field before coming to rest.?

4. An electron with a velocity of 3 x 106 m/s enters into an electric field of 103

N/C. The field is parallel to the velocity of the electron and decelerates it. How far does the electron go before it is brought to a halt?

5. Electron accelerated by potential difference of 100 volts introduced at ‘A’ into a uniform electric field of 104 V/m as shown in figure. The electrons are emerging at the point B in time 4.77 x 10(9 sec. Find (i) Distance AB and (ii) [pic]

6. An electron is projected with an initial velocity of 107 m/s and at an angle 300 to the horizontal into a uniform electric field of 5000 N/C.

a) Find the maximum height to which electron rises vertically.

b) After what horizontal distance does the electron return to its original elevation?

c) The time taken by the particle to reach maximum height. (S-2009)(5) [S-2013] (3)

7. In a Van de Graff generator, a proton starts from rest and is accelerated by an

electric field of 1.2 x 106 N/C over a distance of 4m.

a) What is the acceleration of the proton?

b) What is the velocity of the proton at the end of 4m?

c) How long does it takes for the proton to travel the 4m distance?

8. An electron moving with a speed of 5x106 m/s is shot parallel to an electric field

of strength 103 N/C arranged to retard its motion.

a) How far will the electron travel in the field before coming to rest momentarily?

b) How much time will elapse?

c) If the electric field ends abruptly after 8mm, what fraction of its initial energy will

the electron lose in traversing it?

9. An electron is projected at a velocity of 106m/s between two parallel charged plates. If the electric field between the plates is 1000N/C where will the electron strike the upper plate? The separation of the plates is 0.5cm.

10. A proton has an initial velocity of 2.3 x 105m/s in the x-direction. It enters a uniform electric field of 1.5 x 104 N/C in a direction perpendicular to the lines.

a) Find the time it takes for the proton to travel 0.05 m in x-direction.

b) Find the vertical displacement of the proton after it has traveled 0.05 m in the x-direction.

c) Determine the components of proton velocity after it has traveled 0.05 m in the x-direction.

11. An electron enters the region of a uniform electric field of 200 N/C with an initial velocity 3x 106 m/s. The width of the field region is 0.1m.

a) Find the acceleration of the electron while in the electric field.

b) Find the time it takes the electron to travel through the region of the electric field.

c) What is the vertical displacement of the electron while it is in the electric field?

d) Find the speed of the electron as it emerges from the electric field.

12. An electron enters the region of a uniform electric field of 200 N/C with an initial velocity 8 x 106 m/s. The width of the field region is 0.11m.

a) Find the acceleration of the electron while in the electric field.

b) Find the time it takes the electron to travel through the region of the electric field.

c) What is the vertical displacement of the electron at the end of the electric field?

[Summer 2010](5)

13. An electron beam is accelerated through a potential difference of 2000 volts. Then it is made to pass through a uniform electric field established perpendicular to its path by a set of rectangular parallel plates of length 4 cm. The distance between the plates is 1.5 cm and the potential difference is 50 V. Determine the angle of deflection of the electron beam and its transit time through the electric field.

14. An electron is accelerated through a p.d. 3 kV and enters a uniform magnetic field of 0.03 T acting normal to the direction of electron motion. Determine the radius of path and frequency of oscillation. [Summer 2014](3)

15. *An electron placed in an electric field experiences an upward acceleration of 3.6 x 103 m/s2. Determine the acceleration of a proton in the same electric field. (W/06)

16. An electron is liberated from the lower of the large parallel plates separated by a distance 2 cm. The upper plate has a potential of 2400 V relative to the lower. How long does the electron take to reach it?

17. An electron is projected along the axis midway between the plates of a cathode ray tube with an initial velocity 2 x 107. m/s . The uniform electric field between the plates has an intensity of 20000 N/C and acts upward.

a. How far below the axis has the electron moved when it reaches the end of the

plates?

b. At what angle with the axis is it moving as it leaves the plates?

c. How far below the axis will it strikes the florescent screen?

18. An electron projected at an angle of 37o to the horizontal at an initial speed of

4.5 x 105 m/s in a region of uniform electric field of 200 N/C.

a. Find the time it takes the electron to return to its initial height.

b. Find the maximum height reached by the electron.

c. Find its horizontal displacement when it reaches its maximum height. [W-2012] (5)

19. An electron is projected at a speed of 6 x 106 m/s from lower plate and at an angle 45o into a uniform electric field of 2 x 103 N/C. The field is established by two plane parallel plates of length 10 cm each and separated by 2 cm. The field is directed upwards.

i) Will the electron strike either of the plates?

ii) If it strikes a plate, where does it strike?

20. An electron beam is accelerated through a potential difference of 150V. It is projected into a uniform electric filed product by the application of 20 V to a pair of parallel plates of length 0.1 m and separated by 10-2m. Calculate the deflection of the beam due to the electric field.

21. A singly charged carbon ion moving with a speed of 3 x 105 m/s enters a magnetic field of 7500 G at right angles to the field. Mass of the ion is 19.9 x 10-27 kg.

a) What is the force that acts on the carbon ion?

b) What is the centripetal acceleration of the ion?

c) What is the radius of the circle in which the ion moves?

22. An electron of KE 5 x 103 eV enters a uniform magnetic field of induction 0.32 Wb/m2 perpendicular to its direction f motion. Calculate its velocity and radius of the path.

23. An electron having velocity 106 m/s experiences a maximum force of 1.6 x 10-14 N when it enters a uniform magnetic field. What is the magnitude of magnetic field ?

(W/07)

24. An electron is shot with speed 5 x 106 m/s into a magnetic field at 20o. If the strength of magnetic field is 2 x 10-3 T, describe the motion of the electron.

25. 2keV positron is projected into a uniform field of induction 0.1 T with its velocity vector making an angle of 890 with the field. Find the period, pitch and radius of the helical path of the positron.

26. *An electron shot into a uniform magnetic field at an angle of 60o moves in a spiral of diameter of 10 cm and with a period of 6 x 10-5 s. Determine the electron velocity, the magnetic induction and the pitch of the spiral path.[W-2013](3)

27. A uniform magnetic field of 0.30 T exists along the x-axis. A proton is shot into the field with a speed of 8 x 106m/s at an angle of 300 with the x-axis. Find the radius and pitch of the helical path. [Summer2012](5)

28. A uniform magnetic field of 0.30 T exists along the x-axis. A proton is shot into the field with a speed of 8 x 106m/s at an angle of 00 with the x-axis. Describe the trajectory traced by the particle. [Winter 2014](5)

29. An electron moving with a velocity 106 m/s enters a magnetic field at an angle 200 to the direction of the field. Calculate

a) The value of the magnetic induction so that the radius of helical path be 2 m.

The time required to execute one revolution and

b) The pitch of the spiral.

30. An electron enters the region having [pic]= 0.2 [pic](Tesla). The initial velocity is [pic] x 105 m/s. Find the pitch and radius of the electron trajectory.

31. A 2keV positron is projected into a uniform field of induction 0.10 wb/m2 with its velocity vector making an angle of 600 with magnetic induction. Find the period, the pitch and the radius of the helix if the angle is 2400, what change in above parameters and in helical motion expected?

32. *The electrons circulating in a uniform magnetic field of 4.55x10(4Wb/m[pic] have a kinetic energy of 22.5eV. What are the radius and period of revolution of the electron path? (S/01)

33. What transverse magnetic field acting over the entire length of a cathode ray tube must be applied to cause a deflection of 3 cm on the screen that is 15 cm away from the anode and if the accelerating voltage is 2000V?

34. In a cathode ray tube, the distance from the screen to the centre of the coil is 0.2 m. The length of the field along the axis is 5cm. Calculate the flux density B required to produce a deflection of 1 cm on the screen if the anode voltage is (i) 500 volts and (ii) 1000Volts.

35. An electron passes undeviated through a velocity selector having E=104 V/m and B = 0.02 T. Determine the speed of electron (W/14) (W-09) (3)

36. An electron is accelerated through a potential difference of 1 kV and directed into a region between two parallel plates separated by 0.02m with a 100V potential difference between them. If the electron moves perpendicular to electric field between the plates, what magnetic field is necessary perpendicular to both the electron path and the electric field so that the electron travels in a straight line?

37. *A beam of electron passes undeflected through two mutually perpendicular electric and magnetic fields. If the electric field is cut off and the same magnetic field is maintained, the electron move in a circular path of radius 1.14 cm. determine the ration e/m if E = 8 kV/m and B = 2 x 10(3 T. (W/06)

38. *A positive ion beam moving along the x-axis enters a region of uniform electric field of 3 kV/m along y-axis and magnetic field of 1 KG along z-axis. Calculate the speed of those ions, which pass undeviated. What will happen to ions, which are moving (i) faster, (ii) slower, than these ions? (W/02)

39. *An electron and an alpha particle both move in a circular path in a magnetic field with the same tangential speeds. Compare the numbers of revolutions they make per second, if the mass of the alpha particle is 6.68 x 10(27 kg. (W/06)

40. A proton and α particle with the same KE enter a region of uniform magnetic field moving at right angle to B. Compare the radii of their circular paths. (W-14)

41. The deflection factor of oscilloscope is 35 V/cm. the distance between the deflecting plates to the CRT screen is 16 cm, the length of deflecting plate is 2.5 cm and distance between the deflecting plate is 1.2 cm. What is the accelerating voltage?

42. An electric field of 1500 V/m and a magnetic field of 0.4 wb/m2 act on a moving electron to produce no force. Calculate the velocity of the electron to satisfy the above condition.

43. An [pic] - particle flies into a homogeneous magnetic field perpendicular to its velocity. The angular momentum of the [pic] - particle in the magnetic field is 1.33x10-22 kg.m2/s. The induction of the magnetic field is 2.5x10-2 Wb/m2. Find the Kinetic energy of the [pic] - particle in eV. ( Mass of the [pic] - particle = 6.68x10-27 kg., charge = 3.2x10-19 C)

44. *A proton is moving in a circular orbit of radius 14 cm when placed in a uniform magnetic field of magnitude 0.35 Wb/m2 directed perpendicular to the velocity of the proton. Find the orbital speed of the proton, its angular frequency and its period of revolution. (S/06)

45. What magnetic field would be required to constrain an electron whose energy is 400 eV to a circular path of radius 0.8 m?

46. A proton moves in a vacuum in a uniform magnetic field of strength 100 A/m in a plane perpendicular to magnetic induction lines. Determine the period of revolution of the portion if its, velocity is 1.2 x 103 m/s.

47. An electron with a velocity of 106 m/s enters a uniform magnetic field along the x- direction. One microsecond later it emerges from the magnetic field with a velocity of 106m/s along the y-direction. What is the direction of the magnetic field? What is the average force experienced by the electron?

48. A deuteron an isotope of hydrogen travels in a circular path of radius 40 cm in magnetic field of 1.5 T.

a) Find the speed of deuteron, if its mass is 3.34 x 10-27 kg.

b) Find the time required for it to make half a revolution.

c) Through what potential difference would the deuteron have to be accelerated to acquire this velocity?

49. A proton accelerates from rest in a uniform electric field of 500 V/m. At some later time, its speed is 2.5 x 106 m/s.

Find:

i)acceleration

ii)the time taken by the proton to reach the above speed.

iii)the distance travelled by proton during this time. Summer 2011 (5)

50. The electrons are circulating in a uniform magnetic field of 4.55 x 10-4

wb/m2 have a K.E. of 22.5 eV. What is the radius and period of revolution of the electron path? Summer-2011 (4)

51. An electron beam passes through a magnetic field 2x 10-3 wb/m2 and an electric field of 3.4 x104 V/m. if electron passes undeviated then calculate the velocity of electron.[Summer2012](3) , [Summer2013](3)

52. In a cathode ray tube, the distance from the screen to the centre of the coil is 0.2 m. The length of the field along the axis is 5cm. Calculate the flux density B required to produce a deflection of 1 cm on the screen if the anode voltage is (i) 500 volts and (ii) 1000Volts.

53. The deflection factor of oscilloscope is 35 V/cm. the distance between the deflecting plates to the CRT screen is 16 cm, the length of deflecting plate is 2.5 cm and distance between the deflecting plate is 1.2 cm. What is the accelerating voltage?

54. An electron with a velocity of 4.7x107 m/s enters a uniform magnetic field of induction 0.085 T perpendicular to the field lines. Determine the Lorentz force acting on the electron and radius of of the circle in which it moves. [Winter- 2013] (3)

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4cm

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A + B

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2cm

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12 cm

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