An electron having 450 eV of energy moves at right angles to a uniform magnetic field of flux density 1.50 x 10^-3 T. Find the radius of its circular orbit. [Given: specific charge of the electron = 1.76 x 10⁺¹¹ C/kg]

Ans. 0.048m 

A beam of electrons is under potential difference of 1.36 x 10⁴V applied across two parallel plates 4 cm apart and a magnetic field 2 x 10^-3 T at right angles to each other. If two fields produce no deflection in the electronic beam, calculate (i) The velocity of electrons and (ii) the radius of the orbit in which the beam will move, if the electric field is made zero. [Given; mass of electron = 9.1 x 10^-31 kg.].

Ans: 1.7 x 10⁸m/sec, 0.48m

Calculate the radius of a water drop which would just remain suspended in an electric field of 300 V/cm and charged with one electron.

Ans: 4.9 x 10^-7 m 

An electron beam after being accelerated from rest through a potential difference of 5 kV in vacuum is allowed to impinge normally on a fixed surface. If the incident current is 50μ A, Determine the force exerted on the surface assuming that it brings the electrons to rest. Take the mass of an electron is 9.1 x 10^-31 Kg.

Ans: 1.2 x 10^-8 N 

Calculate the potential difference to be maintained between two horizontal conducting plates separated by a distance of 10 mm so that a small charged oil drop of mass 1.31 x 10^-14 kg will remain in equilibrium. The charge in the oil drop is 6.4 x10^-19C.

Ans: 2046.87 V 

An electron moves in a circular path of radius 20 cm in a uniform magnetic field of 2 x 10^-3T. Find the speed of the electron and the period of revolution. Mass of electron = 9.1x 10^-31kg.

Ans: 7.02 x 10⁷ m/sec and 5.6 x 10⁷ rev/sec 

An electron having 500 eV energy enters at a right angle to a uniform magnetic field of 10⁴ Tesla. If its specific charge is 1.75 x 10¹¹ Ckg^-1, calculate the radius of its circular orbit.

Ans: 0.75 m 

In Millikan's oil drop experiment, a drop is observed to fall with a terminal speed of 1.4 mm/s in the absence of an electric field. When a vertical electric field of 4.9 x 10⁵ v/m is applied, the droplet is observed to continue to move downward at a lower terminal speed of 1.21 mm/s. Calculate the charge on the drop. (Density of oil = 750 kg/m³, viscosity of air =1.81 x 10^-5 kg/ms, density of air = 1.29 kg/m3)

Ans: 5.16 x 10^-19C

A beam of electrons, moving with velocity of 10⁷ m/s, enters midway between two horizontal parallel plates in the direction parallel to the plates which are 5 cm long and 2 cm apart and have a p.d. of V volts between them. Calculate V if the beam is deflected so that it just grazes the edge of the plate. (Assume e/m =1.76 x 10¹¹ c/kg).

Ans: 90.9 V 

An ion for which the charge mass per unit mass is 4.40 x 10⁷ c/kg has a velocity of 3.52 x 10⁵ m/s and moves in a circular orbit in a magnetic field of flux density 0.4T. What will be the radius of this orbit?

Ans: 0.02m

Two plane metal plates 4 cm long are held horizontally 3 cm apart in a vacuum, one being vertically above the other. The upper plate is at a potential of 300 V and the lower plate is earthed. Electrons having a velocity of 10⁷ m/s are injected horizontally midway between the plates and in a direction parallel to 4 cm edge. Calculate the vertical deflection of the electron beam as it emerges from the plates. (e/m for the electron = 1.8 x 10¹¹ Ckg^-1)

Ans: 1.44 x 10^-2 m

An electron moving with a speed of 10⁷ m/s is passed into a magnetic field of intensity 0.1 T normally. What is the radius of the path of the electron inside the field? If the strength of the magnetic field is doubled, what is the radius of the new path? (e/m = 1.8 x 10¹¹C/kg)

Ans: 5.6 x 10^-4m, 2.78 x 10^-4 m 

In a Millikan apparatus the horizontal plates, are 1.5 cm apart. With the electric field switched off an oil drop is observed to fall with the steady velocity of 2.5 x 10^-2 cms^-1. When the field is switched on the upper plate being positive, the drop just remains stationary when the potential difference between the plates is 1500 V. Calculate the radius of the drop and the number of electronic charges neglecting air density. (Given: density of oil = 900 kgm^-3 and viscosity of air = 1.8 x 10^-5 Nsm^-2)

Ans: 1.5 x 10^-6m, 8

An electron is accelerated through a potential difference of 2000 V and then it enters a uniform t magnetic field of 0.02 Testa in a direction perpendicular to it. Find the radius of the path of the electron in the magnetic field. The mass of an electron is 9.1 x 10^-31 kg, the charge of an electron is 1.6 x 10^-19C.

Ans: 7.5 x 10^-3m 

An ion of specific charge 4.40 × 10⁷ C/kg is moving in a circular orbit in a magnetic field of flux density 0.4T with velocity of 3.52 x 10⁵ ms^-1. Calculate the radius of this orbit.

Ans: 0.02 m