Advertisements
Advertisements
Question
An electron is projected horizontally with a kinetic energy of 10 keV. A magnetic field of strength 1.0 × 10−7 T exists in the vertically upward direction.
(a) Will the electron deflect towards the right or left of its motion?
(b) Calculate the sideways deflection of the electron while travelling through 1 m. Make appropriate approximations.
Solution
Given:
The kinetic energy of the electron projected in the horizontal direction, K.E = 10 keV = 1.6 × 10−15 J
Magnetic field, B = 1 × 10−7 T
The direction of magnetic field is vertically upward.
(a) The direction can be found by the right-hand screw rule. So, the electron will be deflected towards left.
(b) Kinetic energy,
`K.E = 1/2mv^2`
`v = sqrt((K.Exx 2)/m)`
Magnetic force,
`vecF = q vecv xx vecB` ......(i)
and F = ma
Therefore, equation (i) will be
`a=(qvecvxx vecB)/m`
Applying equation of motion
`s = ut + 1/2 at^2`
t= Time taken to cross the magnetic field
As there is no force acting on the electron in the horizontal direction, the velocity of the electron remain constant in this direction.
So, the time taken to cross a distance of 1m in the horizontal direction in the magnetic field,
`t = (d)/(v_"horizontal")`
=` (1)/sqrt((2xxkxxE)/m`
= `(qvB)/(4xxK.E)`
`= 1/4 (1.6xx10^-(19) xx1xx10^-7xx sqrt(2 xx K. E)/m)/(10xx 10^-16)`
`= 0.148 xx 10^-3 m`
`= 0.01482 cm`
s = 0.0148 = 1.5 × 10−2 cm
APPEARS IN
RELATED QUESTIONS
State the principle of a cyclotron.
Show that the time period of revolution of particles in a cyclotron is independent of their speeds. Why is this property necessary for the operation of a cyclotron?
An α-particle and a proton are released from the centre of the cyclotron and made to accelerate.
(i) Can both be accelerated at the same cyclotron frequency?
Give reason to justify your answer.
(ii) When they are accelerated in turn, which of the two will have higher velocity at the exit slit of the does?
Explain the principle and working of a cyclotron with the help of a schematic diagram. Write the expression for cyclotron frequency.
Verify that the units weber and volt second are the same.
Which of the following particles will describe the smallest circle when projected with the same velocity perpendicular to a magnetic field?
If a charged particle kept at rest experiences an electromagnetic force,
(a) there must be an electric field
(b) there must be a magnetic field
(c) both fields cannot be zero
(d) both fields can be non-zero
Consider a 10-cm long portion of a straight wire carrying a current of 10 A placed in a magnetic field of 0.1 T making an angle of 53° with the wire. What magnetic force does the wire experience?
Two metal strips, each of length l, are clamped parallel to each other on a horizontal floor with a separation b between them. A wire of mass m lies on them perpendicularly, as shown in the figure. A vertically-upward magnetic field of strength B exists in the space. The metal strips are smooth but the coefficient of friction between the wire and the floor is µ. A current i is established when the switch S is closed at the instant t = 0. Discuss the motion of the wire after the switch is closed. How far away from the strips will the wire reach?
A conducting wire of length l, lying normal to a magnetic field B, moves with a velocity v,as shown in the figure. (a) Find the average magnetic force on a free electron of the wire. (b) Due to this magnetic force, electrons concentrate at one end, resulting in an electric field inside the wire. The redistribution stops when the electric force on the free electrons balances the magnetic force. Find the electric field developed inside the wire when the redistribution stops. (c) What potential difference is developed between the ends of the wire?
(a) An electron moves along a circle of radius 1 m in a perpendicular magnetic field of strength 0.50 T. What would be its speed? Is it reasonable? (b) If a proton moves along a circle of the same radius in the same magnetic field, what would be its speed?
\[\ce{Fe+}\] ions are accelerated through a potential difference of 500 V and are injected normally into a homogeneous magnetic field B of strength 20.0 mT. Find the radius of the circular paths followed by the isotopes with mass numbers 57 and 58. Take the mass of an ion = A (1.6 × 10−27) kg, where A is the mass number.
A cyclotron's oscillator frequency is 10 MHz. What should be the operating magnetic field 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.
Cyclotron is used to ______.
A particle of mass m is moving in a circular path of constant radius r such that, its centripetal acceleration ac is varying with time t as ac = k2rt2, where k is a constant. The power delivered to the particle by the forces acting on it is ______.
