Electricity and Magnetism

# Lorentz force law (mixed fields)

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

A uniform magnetic field $$\vec{B}$$ of magnitude $$1.5\text{ mT}$$ is directed vertically upward. If a proton with kinetic energy $$5.5\text{ MeV}$$ 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 $$1.67 \times 10^{-27} \text{ kg}$$ and $$eV=1.60 \times 10^{-19} \text{ J}.$$ (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 $$950 \text{ V/m},$$ and the magnitude of the magnetic field (directed into the screen) in both the velocity selector and the deflection chamber is $$0.910 \text{ T}.$$ If a singly charged ion with mass $$m=2.20 \times 10^{-25} \text{ kg}$$ 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 $$e=1.60 \times 10^{-19} \text{ C}.$$

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

A proton is traveling in a magnetic field of $$2.30 \text{ mT}$$ with the angle of $$30.0^\circ$$ with respect to the direction of the magnetic field. If the proton experiences a magnetic force of $$6.80 \times 10^{-17} \text{ N},$$ what is the approximate kinetic energy of the proton?

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

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