The angular momentum of a mass distribution where a differential element particle of mass m with velocity v and located at position r is defined in the form /- L = dmr x v = dvpr × v, p= nm where n is the number of particles per unit volume and m is its mass. If each of the particles has a charge q, with their movement they constitute a current J= nqv Show that the relationship between the magnetic dipole moment and the angular momentum is m = L 2m where the magnetic moment is defined dvr x J 2 m =
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- An electron of kinetic energy 0.977 keV circles in a plane perpendicular to a uniform magnetic field. The orbit radius is 35.3 cm. Find (a) the electron's speed, (b) the magnetic field magnitude, (c) the circling frequency, and (d) the period of the motion.An electron of kinetic energy 1.60 keV circles in a plane perpendicular to a uniform magnetic field. The orbit radius is 20.5 cm. Find (a) the electron's speed, (b) the magnetic field magnitude, (c) the circling frequency, and (d) the period of the motion. please highlight each answer when answering: answer (a) with unit answer (b) with unit answer (c) with unit answer (d) with unitsIn the figure, an electron accelerated from rest through potential difference V₁-1.33 kV enters the gap between two parallel plates having separation d = 24.1 mm and potential difference V₂= 175 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap? LI Number(i î+ i Ĵ+ [4]1₂ d V₂ i k) Units <
- An electron of kinetic energy 1.62 keV circles in a plane perpendicular to a uniform magnetic field. The orbit radius is 21.8 cm. Find (a) the electron's speed, (b) the magnetic field magnitude, (c) the circling frequency, and (d) the period of the motion.In the figure, an electron accelerated from rest through potential difference V₁-1.10 kV enters the gap between two parallel plates having separation d = 25.7 mm and potential difference V₂= 104 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap? h Number ( i î+ i d V₂ k) UnitsA 180 V battery is connected across two parallel metal plates of area 28.5 cm2cm2 and separation 7.20mm. A beam of alpha particles (charge +2e+2e, mass 6.64×10-27kg6.64×10-27kg) is accelerated from rest through a potential difference of 1.50 kV and enters the region between the plates perpendicular to the electric field, What magnitude of magnetic field is needed so that the alpha particles emerge undeflected from between the plates? Express your answer with the appropriate units. What is the direction of this magnetic field? The magnetic field is directed out of the page. The magnetic field is directed upward. The magnetic field is directed into the page. The magnetic field is directed downward.
- A particle having mass m = 2.80E-4 kg carries a negative charge q= −1.70E-6 C . The particle is given an initial velocity in the −y direction (downward), as shown in the figure, of v = 7.84E2 m/s. Everywhere in space there is a uniform constant magnetic field B = 0.340 T pointing in the +z direction, which is out of the plane of the page. What is the speed of the particle after 7 periods of the cyclotron motion (in m/s)?In the figure, an electron accelerated from rest through potential difference V1=1.26 kV enters the gap between two parallel plates having separation d = 19.6 mm and potential difference V2= 52.4 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap? I need this in units of mT.In the figure, an electron accelerated from rest through potential difference V1-1.26 kV enters the gap between two parallel plates having separation d = 19.6 mm and potential difference V2- 52.4 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap? Number ( o ĵ+ i R) Units mT 124.7