Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given:-
Mass of the particle = m
Positive charge on the particle = q
Uniform velocity of the particle = v
Magnetic field = B
(a) The radius of the circular arc described by the particle in the magnetic field:-
We know
`r = (mv)/(qB)`
(b) 
The angle subtended by the arc at the centre:-
Line MAB is tangent to arc ABC, so the angle described by the charged particle,
∠MAO = 90°
Now, ∠NAC = 90°
OAC = OCA = θ
[by geometry]
Then, AOC = 180° − (θ + θ) (By angle-sum property of a triangle)
= π − 2θ
(c) The time for which the particle stay inside the magnetic field:-
Distance covered by the particle inside the magnetic field,
l = rθ
`t = 1/v = m/(qB)(pi - 2theta)(U sing r = (mv)/(qB))`
(d) If the charge q on the particle is negative, then
(i) Radius of circular arc, `r = (mv)/(qB)`
(ii) The centre of the arc will lie within the magnetic field. Therefore, the angle subtended by the arc = π + 2θ
(iii) Similarly, the time taken by the particle to cover the path inside the magnetic field = `m/(qB)(pi + 2theta)`
APPEARS IN
संबंधित प्रश्न
Write the expression for the force `vecF` acting on a particle of mass m and charge q moving with velocity `vecV` in a magnetic field `vecB` , Under what conditions will it move in (i) a circular path and (ii) a helical path?
Show that the kinetic energy of the particle moving in a magnetic field remains constant.
A proton and a deuteron having equal momenta enter in a region of a uniform magnetic field at right angle to the direction of a the field. Depict their trajectories in the field.
Assume that the magnetic field is uniform in a cubical region and zero outside. Can you project a charged particle from outside into the field, so that the particle describes a complete circle in the field?
If a charged particle projected in a gravity-free room deflects,
(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
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
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 i is passed through a silver strip of width d and area of cross-section A. The number of free electrons per unit volume is n. (a) Find the drift velocity v of the electrons. (b) If a magnetic field B exists in the region, as shown in the figure, what is the average magnetic force on the free electrons? (c) Due to the magnetic force, the free electrons get accumulated on one side of the conductor along its length. This produces a transverse electric field in the conductor, which opposes the magnetic force on the electrons. Find the magnitude of the electric field which will stop further accumulation of electrons. (d) What will be the potential difference developed across the width of the conductor due to the electron-accumulation? The appearance of a transverse emf, when a current-carrying wire is placed in a magnetic field, is called Hall effect.
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?
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.
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 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)`
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 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.
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.
When does a moving charged particle nor experience any force while moving through a uniform magnetic field?
A uniform magnetic field of 1.5 T exists in a cylindrical region of radius 10.0 cm, its direction parallel to the axis along east to west. A wire carrying current of 7.0 A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if,
(a) the wire intersects the axis,
(b) the wire is turned from N-S to northeast-northwest direction,
(c) the wire in the N-S direction is lowered from the axis by a distance of 6.0 cm?
A particle of mass 10 mg and having a charge of 50 mC is projected with a speed of 15 m/s into a uniform magnetic field of 125 mT. Assuming that the particle is projected with its velocity perpendicular to the magnetic field, the time after which the particle reaches its original position for the first time is ______.
