Physics

Physics · electromagnetism

Problem

A. An electron after leaving a device, which accelerated it with the potential difference

U

, falls into a region with an inhomogeneous field

\boldsymbol{B}

generated with a system of stationary coils

L_{1}, L_{2}, \ldots, L_{n}

. The known currents in the coils are

i_{1}, i_{2}, \ldots, i_{n}

, respectively. What should the currents

i_{1}

i_{2}

\ldots, i_{n}

' in the coils

L_{1}, L_{2}, \ldots, L_{n}

be, in order to guide the proton (initially accelerated with the potential difference

-U

) along the same trajectory (and in the same direction) as that of the electron? HINT: The problem can be solved by finding a condition under which the equation describing the trajectory is the same in both cases. It may be helpful to use the relation:

\boldsymbol{p} \frac{d}{d t} \boldsymbol{p}=\frac{1}{2} \frac{d}{d t} \boldsymbol{p}^{2}=\frac{1}{2} \frac{d}{d t} p^{2}

Given constants: The problem concerns investigation of transforming the electron microscope with magnetic guiding of the electron beam (which is accelerated with the potential difference

U=

511 \mathrm{kV}

) into a proton microscope (in which the proton beam is accelerated with the potential difference

-U

). For this purpose, solve the following two problems:

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