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Magnetic Fields

Magnets have bewildered everyone from the Insane Clown Posse to Tim Allen. Stand apart from the madding crowd and set yourself straight on the fields of moving charges.

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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