Advertisements
Advertisements
Question
An electron of kinetic energy 100 eV circulates in a path of radius 10 cm in a magnetic field. Find the magnetic field and the number of revolutions per second made by the electron.
Advertisements
Solution
Given:
Kinetic energy of an electron = 100 eV
Radius of the circle = 10 cm
`1/2mv^2` = 100 eV = 1.6 × 10−17 J (1 eV = 1.6 × 10−19 J)
Here,
m is the mass of an electron and v is the speed of an electron. Thus,
1/2 × 9.1 × 10−31 × v2 = 1.6 × 10−17 J
⇒ v2 = 0.35 × 1014
v = 0.591 × 107 m/s
Now,
`r = (mv)/(eB)`
`⇒ B = (mv)/(er)`
`= (9.1xx10^-31xx0.591xx10^7)/(1.6xx10^-19xx0.1)`
B = 3.3613 × 10−4 T
Therefore, the applied magnetic field = 3.4 × 10−4 T
Number of revolutions per second of the electron,
`f = 1/T`
`T = (2pir)/v= 2pim/(eB)`
`T = (2pim)/Be`
`f = (Be)/(2pim)`
`=( 3.4xx10^-4xx1.6xx10^-19)/(2xx3.14xx9.1xx10^-31`
= 0.094 × 108
= 9.4 × 106
f = 9.4 × 106
APPEARS IN
RELATED QUESTIONS
An electron moving horizontally with a velocity of 4 ✕ 104 m/s enters a region of uniform magnetic field of 10−5 T acting vertically upward as shown in the figure. Draw its trajectory and find out the time it takes to come out of the region of magnetic
field.
Write the expression for Lorentz magnetic force on a particle of charge ‘q’ moving with velocity `vecv` in a magnetic field`vecB`. Show that no work is done by this force on the charged particle.
A positively-charged particle projected towards east is deflected towards north by a magnetic field. The field may be
A beam consisting of protons and electrons moving at the same speed goes through a thin region in which there is a magnetic field perpendicular to the beam. The protons and the electrons
A charged particle moves in a uniform magnetic field. The velocity of the particle at some instant makes an acute angle with the magnetic field. The path of the particle will be
A particle is projected in a plane perpendicular to a uniform magnetic field. The area bounded by the path described by the particle is proportional to
Two particles X and Y having equal charge, after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii R1 and R2 respectively. The ratio of the mass of X to that of Y is ______.
A 10 g bullet with a charge of 4.00 μC is fired at a speed of 270 m s−1 in a horizontal direction. A vertical magnetic field of 500 µT exists in the space. Find the deflection of the bullet due to the magnetic field as it travels through 100 m. Make appropriate approximations.
A current of 2 A enters at the corner d of a square frame abcd of side 20 cm and leaves at the opposite corner b. A magnetic field B = 0.1 T exists in the space in a direction perpendicular to the plane of the frame, as shown in the figure. Find the magnitude and direction of the magnetic forces on the four sides of the frame.
A semicircular wire of radius 5.0 cm carries a current of 5.0 A. A magnetic field B of magnitude 0.50 T exists along the perpendicular to the plane of the wire. Find the magnitude of the magnetic force acting on the wire.
A metal wire PQ of mass 10 g lies at rest on two horizontal metal rails separated by 4.90 cm (figure). A vertically-downward magnetic field of magnitude 0.800 T exists in the space. The resistance of the circuit is slowly decreased and it is found that when the resistance goes below 20.0 Ω, the wire PQ starts sliding on the rails. Find the coefficient of friction.
Consider a non-conducting ring of radius r and mass m that has a total charge qdistributed uniformly on it. The ring is rotated about its axis with an angular speed ω. (a) Find the equivalent electric current in the ring. (b) Find the magnetic moment µ of the ring. (c) Show that `pi = (q)/(2m)` l, where l is the angular momentum of the ring about its axis of rotation.
A charged particle is accelerated through a potential difference of 12 kV and acquires a speed of 1.0 × 106 m s−1. It is then injected perpendicularly into a magnetic field of strength 0.2 T. Find the radius of the circle described by it.
A particle moves in a circle of diameter 1.0 cm under the action of a magnetic field of 0.40 T. An electric field of 200 V m−1 makes the path straight. Find the charge/mass ratio of the particle.
The velocity of a body of mass 2 kg as a function of time t is given by v(t) = 2t`hat"i" + "t"^2hat"j"`. The force acting on it, at time t = 2 s is given by ______.
