At time t1, an electron is sent along the positive direction of an x-axis, through both an electric field and a magnetic field, with directed parallel to the y-axis. Figure 28-33 gives the y component Fnet, y of the net force on the electron due to the two fields, as a function of theelectron’s speed v at time t1.The scale of the velocity axis is set by 100.0 m/s. The x and z components of the net force are zero at t1. Assuming , find
(a)the magnitude E and
(b )in unit-vector notation.
The direction of the magnetic force is perpendicular to the plane formed by and as determined by the right-hand rule.
Right Hand Rule states that if we arrange our thumb, forefinger, and middle finger of the right-hand perpendicular to each other, then the thumb points towards the direction of the motion of the conductor relative to the magnetic field, and the forefinger points towards the direction of the magnetic field and the middle finger points towards the direction of the induced current.
Formulae are as follows:
Where F is a magnetic force, v is velocity, E is the electric field, B is the magnetic field, and q is the charge of the particle.
To find the magnitude of E:
Hence, the magnitude of E is
To find a magnetic field :
To find the direction of role="math" localid="1663013448881" ,
The net force is directed in direction and velocity in direction, so by applying the right-hand rule, must be directed in direction.
Hence, the magnetic field is .
Therefore, the magnitude of the electric field and magnetic field can be determined by using the respective formulae. The direction of the magnetic field can be found by using the right-hand rule.
An alpha particle can be produced in certain radioactive decays of nuclei and consists of two protons and two neutrons. The particle has a charge of and a mass of , where is the atomic mass unit, with kg. Suppose an alpha particle travels in a circular path of radius cm in a uniform magnetic field with . Calculate (a) its speed (b) its period of revolution, (c) its kinetic energy, and (d)the potential difference through which it would have to be accelerated to achieve this energy.
Figure 28-46 shows a wood cylinder of mass and length , with turns of wire wrapped around it longitudinally, so that the plane of the wire coil contains the long central axis of the cylinder. The cylinder is released on a plane inclined at an angle to the horizontal, with the plane of the coil parallel to the incline plane. If there is a vertical uniform magnetic field of magnitude , what is the least current i through the coil that keeps the cylinder from rolling down the plane?
Figure 28-31 gives snapshots for three situations in which a positively charged particle passes through a uniform magnetic field . The velocities of the particle differ in orientation in the three snapshots but not in magnitude. Rank the situations according to (a) the period, (b) the frequency, and (c) the pitch of the particle’s motion, greatest first.
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