Advertisements
Advertisements
प्रश्न
Find the condition under which the charged particles moving with different speeds in the presence of electric and magnetic field vectors can be used to select charged particles of a particular speed.
Advertisements
उत्तर
Force in the presence of magnetic and electric field is given as
`vecF=q(vecE+vecv xx vecB)`
Consider that the electric and the magnetic field are perpendicular to each other and, also, perpendicular to the velocity of the particle.
`vecE=Ehatj,vecB=Bhatk,vecB,vecv=vhati`
Then we have :`vec(F_E)=qvecE=qEhatj, vec(F_B)=q vecv xx vecB, =q(vhatixxBhatk)=-qBhatj`
`therefore vecF=q(E-vB)hatj`
If we adjust the values of `vecE` and `vecB` such that magnitudes of the two forces are equal, then the total force on the charge will be zero and it will move in the fields undeflected. This happens when
qE = qvB
`therefore v=E/B`
The above condition can be used to select a charged particle of particular velocity from the charges moving with different speeds. Therefore, it is called velocity selector.
संबंधित प्रश्न
Two identical coils P and Q each of radius R are lying in perpendicular planes such that they have a common centre. Find the magnitude and direction of the magnetic field at the common centre of the two coils, if they carry currents equal to I and \[\sqrt{3}\] I respectively.
A point charge q moving with speed v enters a uniform magnetic field B that is acting into the plane of the paper as shown. What is the path followed by the charge q and in which plane does it move?
If an electric field \[\vec{E}\] is also applied such that the particle continues moving along the original straight line path, what should be the magnitude and direction of the electric field \[\vec{E}\] ?
The motion of copper plate is damped when it is allowed to oscillate between the two poles of a magnet. What is the cause of this damping?
Two long straight parallel conductors carrying steady currents I1 and I2 are separated by a distance 'd'. Explain briefly, with the help of a suitable diagram, how the magnetic field due to one conductor acts on the other. Hence deduce the expression for the force acting between the two conductors. Mention the nature of this force.
A wire ab of length l, mass m and resistance R slides on a smooth, thick pair of metallic rails joined at the bottom as shown in figure. The plane of the rails makes an angle θ with the horizontal. A vertical magnetic field B exists in the region. If the wire slides on the rails at a constant speed v, show that \[B = \sqrt{\frac{mg R sin\theta}{v l^2 \cos^2 \theta}}\]
Consider the situation shown in figure. The wires P1Q1 and P2Q2 are made to slide on the rails with the same speed 5 cm s−1. Suppose the 19 Ω resistor is disconnected. Find the current through P2Q2 if (a) both the wires move towards right and (b) if P1Q1 moves towards left but P2Q2 moves towards right.
A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
A moving charge will gain kinetic energy due to the application of ______.
A charged particle is accelerated through a potential difference of 12 kV and acquires a speed of 106 ms-1. It is projected perpendicularly into the magnetic field of strength 0.2 T. The radius of the circle described is ______ cm.
