Advertisements
Advertisements
प्रश्न
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 ______.
विकल्प
(R1/R2)1/2
R1/R2
(R1/R2)2
R1R2.
Advertisements
उत्तर
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 (R1/R2)2.
Explanation:
`"R"_1^2/"R"_2^2`
Particles X and Y of respective masses m1 and m2 are carrying charge q describing circular paths with respective radii R1 and R2 such that
`"R"_1 = ("m"_1"v"_1)/"qB"`
`"R"_2 = ("m"_2"v"_2)/"qB"`
Since both the particles are accelerated through the same potential difference, both will have the same kinetic energy.
`therefore 1/2 "m"_1"v"_1^2 = 1/2 "m"_2"v"_2^2`
`because "R"_1 = ("m"_1"v"_1)/"qB" => "v"_1 = ("R"_1"qB")/"m"_1`
And
`because "R"_2 = ("m"_2"v"_2)/"qB" => "v"_2 = ("R"_2"qB")/"m"_2`
`therefore "m"_1 (("R"_1 "qB")/"m"_1)^2 = "m"_2 (("R"_1 "qB")/"m"_1)^2`
`=> "m"_1/"m"_2 = "R"_1^2/"R"_2^2`
APPEARS IN
संबंधित प्रश्न
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
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
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
A magnetic field of \[(4.0\times10^-3 \overrightarrow k)\] T exerts a force of \[(4.0 \overrightarrow i + 3.0 \overrightarrow j ) \times 10^{−10} N\] on a particle with a charge of 1.0 × 10−9 C and going in the x − y plane. Find the velocity of the particle.
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?
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 magnetic field of strength 1.0 T is produced by a strong electromagnet in a cylindrical region of radius 4.0 cm, as shown in the figure. A wire, carrying a current of 2.0 A, is placed perpendicular to and intersecting the axis of the cylindrical region. Find the magnitude of the force acting on the wire.
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 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 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 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.
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.
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?
