Advertisements
Advertisements
Question
A particle of mass m and charge q is projected into a region that has a perpendicular magnetic field B. Find the angle of deviation (figure) of the particle as it comes out of the magnetic field if the width d of the region is very slightly smaller than
(a) `(mv)/(qB)` (b)`(mv)/(2qB)` (c)`(2mv)/(qB)`
Advertisements
Solution
Given:
Mass of the particle = m
Charge of the particle = q
Magnetic field = B
As per the question, the particle is projected into a perpendicular magnetic field.
(a) When the width, d = `(mv)/(qB)`
d is equal to the radius and θ is the angle between the radius and tangent, which is equal to `pi/2`.
(b) When the width, d = `(mv)/(2qB)`
Width of the region in which a magnetic field is applied is half of the radius of the circular path described by the particle.
As the magnetic force is acting only along the y direction, the velocity of the particle will remain constant along the x direction. So, if d is the distance travelled along the x axis, then
d = vxt
`t = (d)/(V_x)`.........(i))
(i)
(ii)
The acceleration along the x direction is zero. The force will act only along the y direction.
Using the equation of motion for motion along the y axis:
vy = uy + ayt
`vy = 0 + (qu_xBt)/(m)`
`= (qu_xBt)/m`
Putting the value of t from equation (i), we get:
`(qu_xBd)/(mv_x)`
we know
`tantheta = (vy)/(vx)`
`(qBd)/(mv_x) = (qBmv_x)/(2qBmvx) = 1/2`
`⇒theta = tan^-1(1/2)`
`= 26.4 = 30^circ = pi/6`
(c) When the width, d = (c) When the width, d = `(2mv)/(qB)`
APPEARS IN
RELATED QUESTIONS
Show that the kinetic energy of the particle moving in a magnetic field remains constant.
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.
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 along a circle under the action of possible constant electric and magnetic fields. Which of the following is possible?
(a) E = 0, B = 0
(b) E = 0, B ≠ 0
(c) E ≠ 0, B = 0
(d) E ≠ 0, B ≠ 0
If a charged particle moves unaccelerated in a region containing electric and magnetic fields
(a) `vecE "must be perpendicular" to vecB`
(b) `vecv "must be perpendicular" to vecE`
(c) must be perpendicular to v_B
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
An experimenter's diary reads as follows: "A charged particle is projected in a magnetic field of `(7.0 vec i - 3.0 vecj)xx 10^-3 `T. The acceleration of the particle is found to be `(x veci + 7.0 vecj )` The number to the left of i in the last expression was not readable. What can this number 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.
Using the formula \[\vec{F} = q \vec{v} \times \vec{B} \text{ and } B = \frac{\mu_0 i}{2\pi r}\]show that the SI units of the magnetic field B and the permeability constant µ0 may be written as N mA−1 and NA−2 respectively.
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 circular coil of radius 2.0 cm has 500 turns and carries a current of 1.0 A. Its axis makes an angle of 30° with the uniform magnetic field of magnitude 0.40 T that exists in the space. Find the torque acting on the coil.
A narrow beam of singly charged potassium ions of kinetic energy 32 keV is injected into a region of width 1.00 cm with a magnetic field of strength 0.500 T, as shown in the figure. The ions are collected at a screen 95.5 cm away from the field region. If the beam contains isotopes of atomic weights 39 and 41, find the separation between the points where these isotopes strike the screen. Take the mass of a potassium ion = A (1.6 × 10−27) kg, where A is the mass number.
Doubly-ionised helium ions are projected with a speed of 10 km s−1 in a direction perpendicular to a uniform magnetic field of magnitude 1.0 T. Find (a) the force acting on an ion (b) the radius of the circle in which it circulates and (c) the time taken by an ion to complete the circle.
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 uniform magnetic field of magnitude 0.20 T exists in space from east to west. With what speed should a particle of mass 0.010 g and with charge 1.0 × 10−5 C be projected from south to north so that it moves with uniform velocity?
A particle with a charge of 5.0 µC and a mass of 5.0 × 10−12 kg is projected with a speed of 1.0 km s−1 in a magnetic field of magnitude 5.0 mT. The angle between the magnetic field and the velocity is sin−1 (0.90). Show that the path of the particle will be a helix. Find the diameter of the helix and its pitch.
Current flows through uniform, square frames as shown in the figure. In which case is the magnetic field at the centre of the frame not zero?
