Lorentz force law (mixed fields)


Consider a charged particle moving in a magnetic field with a constant velocity of 20i^ km/s,20\hat{i} \text{ km/s}, in a direction perpendicular to the magnetic field. The mass and charge of the particle is 13 g13\text{ g} and 75μC,75\,\mu\text{C}, respectively. If the free-fall acceleration in the magnetic field region is 9.8j^ m/s2,-9.8\hat{j} \text{ m/s}^2, what is the appropriate magnetic field?

A uniform magnetic field B\vec{B} of magnitude 1.5 mT1.5\text{ mT} is directed vertically upward. If a proton with kinetic energy 5.5 MeV5.5\text{ MeV} enters the chamber horizontally, what is the approximate magnetic deflecting force acting on the proton as it enters the magnetic field?

The proton mass is 1.67×1027 kg1.67 \times 10^{-27} \text{ kg} and eV=1.60×1019 J.eV=1.60 \times 10^{-19} \text{ J}. (Neglect Earth's magnetic field.)

The above is a schematic diagram of a mass spectrometer. The magnitude of the electric field between the plates of the velocity selector is 950 V/m,950 \text{ V/m}, and the magnitude of the magnetic field (directed into the screen) in both the velocity selector and the deflection chamber is 0.910 T.0.910 \text{ T}. If a singly charged ion with mass m=2.20×1025 kgm=2.20 \times 10^{-25} \text{ kg} passes the velocity selector region with no deflection, what is the approximate radius of the path in deflection chamber?

The value of the elementary charge is e=1.60×1019 C.e=1.60 \times 10^{-19} \text{ C}.

In the above diagram, a charged particle with mass m=1.4×1015 kgm=1.4 \times 10^{-15} \text{ kg} and charge q=2.6×1017 Cq=2.6 \times 10^{-17} \text{ C} enters a region of uniform magnetic field B=0.8 TB=0.8 \text{ T} (directed into the screen) and uniform electric field (directed downward). If the particle with a speed of v=15.0 m/sv=15.0 \text{ m/s} passes through the device with no deflection, what is the magnitude of the electric field?

A proton is traveling in a magnetic field of 2.30 mT2.30 \text{ mT} with the angle of 30.030.0^\circ with respect to the direction of the magnetic field. If the proton experiences a magnetic force of 6.80×1017 N,6.80 \times 10^{-17} \text{ N}, what is the approximate kinetic energy of the proton?

The proton mass is 1.67×1027 kg1.67 \times 10^{-27} \text{ kg} and the value of the elementary charge is e=1.60×1019 C.e=1.60 \times 10^{-19} \text{ C}.


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