True or false on monopoles and flux

Problem

State whether each statement is true or false: (a) isolated magnetic monopoles exist in nature; (b) the flux of $\vec B$ through a closed surface is always zero; (c) a charge moving parallel to $\vec B$ experiences no magnetic force; (d) the Lorentz force does work on the charge it acts on.

Solution

(a) FALSE: isolated magnetic monopoles are not observed in nature; the sources of the magnetic field are always dipoles (inseparable north and south poles).

(b) TRUE: precisely because monopoles do not exist, the lines of $\vec B$ are always closed and the flux through any closed surface is zero, $\Phi_B = 0$.

(c) TRUE: if $\vec v\parallel\vec B$ then $\sin\theta = 0$ and hence $F = |q|vB\sin\theta = 0$.

(d) FALSE: the Lorentz force is always perpendicular to the velocity ($\vec F\perp\vec v$), so its work is zero and the kinetic energy of the charge does not change. $\ev{\text{F, T, T, F}}$

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Topics: Magnetismo Concepts: Campo magnetico · Forza di Lorentz