Advertisements
Advertisements
Question
A narrow beam of singly-charged carbon ions, moving at a constant velocity of 6.0 × 104m s−1, is sent perpendicularly in a rectangular region of uniform magnetic field B = 0.5 T (figure). It is found that two beams emerge from the field in the backward direction, the separations from the incident beam being 3.0 cm and 3.5 cm. Identify the isotopes present in the ion beam. Take the mass of an ion = A(1.6 × 10−27) kg, where A is the mass number.
Advertisements
Solution
Given:
Velocity of a narrow beam of singly-charged carbon ions, v = 6.0 × 104 m s−1
Strength of magnetic field B = 0.5 T
Separations between the two beams from the incident beam are 3.0 cm and 3.5 cm.
Mass of an ion = A(1.6 × 10−27) kg
The radius of the curved path taken by the first beam, r_1 = `(m_1v)/(qB)`
where m1 is the mass of the first isotope and q is the charge.
For the second beam:
`r_2 = (m_2v)/(qB)`
where m2 is the mass of the first isotope and q is the charge.
`(r_1)/(r_2) =(m_1)/(qB)`
`(3//2)/(3.5//2) =
(A_1xx1.6xx10^-27)/(A_2xx1.6xx10^-27)`
`6/7 = (A_1)/(A_2)`
As
`r_1 = (m_1v)/(qB)`
⇒ `m_1 = (q_Br_1)/v`
⇒ `(1.6xx10^-19xx0.5xx0.015)/(6xx10^-27)`
= 20 × 10-27 kg
= `(20xx10^-27)/(1.6xx10^-27)u`
= 12.5 u
Also
`A_2 = 7/6A_1`
=` 7/6 xx 12.5`
= 14.58 u
So, the two isotopes of carbon used are 12C6 and 14C6.
APPEARS IN
RELATED QUESTIONS
Write the expression, in a vector form, for the Lorentz magnetic force \[\vec{F}\] due to a charge moving with velocity \[\vec{V}\] in a magnetic field \[\vec{B}\]. What is the direction of the magnetic force?
Show that the kinetic energy of the particle moving in a magnetic field remains constant.
A proton and an α-particle move perpendicular to a magnetic field. Find the ratio of radii of circular paths described by them when both have (i) equal velocities, and (ii) equal kinetic energy.
A flexible wire of irregular shape, abcd, as shown in the figure, turns into a circular shape when placed in a region of magnetic field which is directed normal to the plane of the loop away from the reader. Predict the direction of the induced current in the wire.
A positively-charged particle projected towards east is deflected towards north by a magnetic field. The field may be
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
When a proton is released from rest in a room, it starts with an initial acceleration a0towards west. When it is projected towards north with a speed v0, it moves with an initial acceleration 3a0 towards west. Find the electric field and the maximum possible magnetic field in the room.
A wire, carrying a current i, is kept in the x−y plane along the curve y = A sin `((2x)/lamda x)`. magnetic field B exists in the z direction. Find the magnitude of the magnetic force on the portion of the wire between x = 0 and x = λ.
A proton describes a circle of radius 1 cm in a magnetic field of strength 0.10 T. What would be the radius of the circle described by an α-particle moving with the same speed in the same magnetic field?
Protons with kinetic energy K emerge from an accelerator as a narrow beam. The beam is bent by a perpendicular magnetic field, so that it just misses a plane target kept at a distance l in front of the accelerator. Find the magnetic field.
A square coil of edge l and with n turns carries a current i. It is kept on a smooth horizontal plate. A uniform magnetic field B exists parallel to an edge. The total mass of the coil is M. What should be the minimum value of B for which the coil will start tipping over?
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 of mass m and positive charge q, moving with a uniform velocity v, enters a magnetic field B, as shown in the figure. (a) Find the radius of the circular arc it describes in the magnetic field. (b) Find the angle subtended by the arc at the centre. (c) How long does the particle stay inside the magnetic field? (d) Solve the three parts of the above problem if the charge q on the particle is negative.
A proton is projected with a velocity of 3 × 106 m s−1 perpendicular to a uniform magnetic field of 0.6 T. Find the acceleration of the proton.
The figure shows a convex lens of focal length 12 cm lying in a uniform magnetic field Bof magnitude 1.2 T parallel to its principal axis. A particle with charge 2.0 × 10−3 C and mass 2.0 × 10−5 kg is projected perpendicular to the plane of the diagram with a speed of 4.8 m s−1. The particle moves along a circle with its centre on the principal axis at a distance of 18 cm from the lens. Show that the image of the particle moves along a circle and find the radius of that circle.
Two particles, each with mass m are placed at a separation d in a uniform magnetic field B, as shown in the figure. They have opposite charges of equal magnitude q. At time t = 0, the particles are projected towards each other, each with a speed v. Suppose the Coulomb force between the charges is switched off. (a) Find the maximum value vmof the projection speed, so that the two particles do not collide. (b) What would be the minimum and maximum separation between the particles if v = vm/2? (c) At what instant will a collision occur between the particles if v = 2vm? (d) Suppose v = 2vm and the collision between the particles is completely inelastic. Describe the motion after the collision.
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.
A particle of mass m and charge q is released from the origin in a region in which the electric field and magnetic field are given by
`vecB = -B_0 vecj and vecE = E_0 vecK `
Find the speed of the particle as a function of its z-coordinate.
A long, straight wire carrying a current of 30 A is placed in an external, uniform magnetic field of 4.0 × 10−4 T parallel to the current. Find the magnitude of the resultant magnetic field at a point 2.0 cm away from the wire.
