Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given:-
Magnetic field, B = `(4xx10xx^-3 hatK)`T
Force exerted by the magnetic field on the charged particle, F = `(4 hati + 3hatj )`× 10−10 N
Charge of the particle, q = 1 × 10−9 C
As per the question, the charge is going in the X-Y plane.
So, the x-component of force, Fx = 4 × 10−10 N
and the y-component of force, Fy = 3 × 10−10 N
Considering the motion along x-axis:-
Fx = qvy×B
On putting the respective values, we get:-
vy = 100 m/s
Motion along y-axis:-
Fy = qvx×B
⇒ vx = 75 m/s
Thus, total velocity =`( -75 vec i + 100 vec j) `m/s
APPEARS IN
संबंधित प्रश्न
A moving charged particle q travelling along the positive x-axis enters a uniform magnetic field B.
When will the force acting on q be maximum?
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 straight wire of mass 200 g and length 1.5 m carries a current of 2 A. It is suspended in mid air by a uniform magnetic field B. What is the magnitude of the magnetic field?
A positively-charged particle projected towards east is deflected towards north by a magnetic field. The field may be
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 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
Consider three quantities \[x = E/B, y = \sqrt{1/ \mu_0 \epsilon_0}\] and \[z = \frac{l}{CR}\] . Here, l is the length of a wire, C is a capacitance and R is a resistance. All other symbols have standard meanings.
(a) x, y have the same dimensions.
(b) y, z have the same dimensions.
(c) z, x have the same dimensions.
(d) None of the three pairs have the same dimensions.
Prove that the force acting on a current-carrying wire, joining two fixed points a and b in a uniform magnetic field, is independent of the shape of 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.
Consider a non-conducting ring of radius r and mass m that has a total charge qdistributed uniformly on it. The ring is rotated about its axis with an angular speed ω. (a) Find the equivalent electric current in the ring. (b) Find the magnetic moment µ of the ring. (c) Show that `pi = (q)/(2m)` l, where l is the angular momentum of the ring about its axis of rotation.
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.
Electrons emitted with negligible speed from an electron gun are accelerated through a potential difference V along the x-axis. These electrons emerge from a narrow hole into a uniform magnetic field B directed along this axis. However, some of the electrons emerging from the hole make slightly divergent angles, as shown in the figure. Show that these paraxial electrons are refocussed on the x-axis at a distance `sqrt(8pi^2mV)/(eB^2).`
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 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.
An electron is emitted with negligible speed from the negative plate of a parallel-plate capacitor charged to a potential difference V. The separation between the plates is dand a magnetic field B exists in the space, as shown in the figure. Show that the electron will fail to strike the upper plates if `d > ((2m_eV)/(eB_0^2))^(1/2)`
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 ______.
