Magnetic field and Lorentz force

An electron moves with speed $v=5.0\cdot 10^{5}m/s$ perpendicular to a uniform magnetic field $B=0.40\mathrm{T}$. Compute the magnitude of the magnetic force on the electron.

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A proton moves with speed $v=2.0\cdot 10^{6}m/s$ in a uniform magnetic field $B=0.30\mathrm{T}$; the velocity forms an angle of $45^{\circ }$ with the field. Compute the magnitude of the magnetic force on the proton.

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A proton, of mass $m_p=1.67\cdot 10^{-27}\mathrm{kg}$, moves with speed $v=2.0\cdot 10^{6}m/s$ perpendicular to a uniform magnetic field $B=0.50\mathrm{T}$. Compute the radius of the trajectory and the period of the motion.

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Compute the cyclotron frequency of an electron in a uniform magnetic field $B=0.10\mathrm{T}$, and determine whether it depends on the speed of the electron.

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An electron, initially at rest, is accelerated by the potential difference $\Delta V=500\mathrm{V}$ and enters perpendicularly a uniform magnetic field $B=1.0\cdot 10^{-3}\mathrm{T}$. Compute the radius of the trajectory.

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A proton, of mass $m_p=1.67\cdot 10^{-27}\mathrm{kg}$, enters a uniform magnetic field $B=0.050\mathrm{T}$ with velocity $v=3.0\cdot 10^{5}m/s$ forming an angle of $60^{\circ }$ with the field. Compute the radius and the pitch of the helix.

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In a velocity selector the electric field equals $E=5.0\cdot 10^{3}V/m$. Compute the magnetic field needed for the particles with speed $v=2.5\cdot 10^{5}m/s$ to cross the selector without being deflected.

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In a mass spectrometer ions of charge $e$, starting practically at rest, are accelerated by the potential difference $\Delta V=1.0\mathrm{kV}$ and enter a uniform magnetic field $B=0.20\mathrm{T}$ perpendicular to the velocity, where they describe a semicircle of radius $r=12.0\mathrm{cm}$. Compute the mass of the ions in kilograms and in atomic mass units ($1\mathrm{u}=1.66\cdot 10^{-27}\mathrm{kg}$).

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An aluminum strip of thickness $s=0.10\mathrm{mm}$ carries the current $I=8.0\mathrm{A}$ in a magnetic field $B=1.2\mathrm{T}$ perpendicular to its wide faces, and the Hall voltage $\Delta V_H=3.3\mu \mathrm{V}$ is measured between its edges. Compute the density of the carriers, of charge $-e$.

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A wire in the shape of a quarter circle of radius $R=0.20\mathrm{m}$, carrying the current $I=3.0\mathrm{A}$, lies in a plane perpendicular to a uniform magnetic field $B=0.50\mathrm{T}$. Compute the magnitude of the force on the wire.

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A horizontal rod of length $\ell =0.20\mathrm{m}$ and mass $m=10\mathrm{g}$ hangs from two insulating vertical threads in a uniform horizontal magnetic field $B=0.40\mathrm{T}$, perpendicular to the rod. Compute the current that makes the tension in the threads vanish.

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A circular coil of $N=20$ turns of radius $r=3.0\mathrm{cm}$ carries the current $I=1.5\mathrm{A}$ in a uniform magnetic field $B=0.60\mathrm{T}$ parallel to the plane of the coil. Compute the torque on the coil.

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A coil with magnetic moment $\mu =0.25\mathrm{A}\cdot {\mathrm{m}}^2$ is in stable equilibrium in a uniform magnetic field $B=0.80\mathrm{T}$. Compute the work needed to rotate it slowly until the magnetic moment forms an angle of $120^{\circ }$ with the field.

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