Problem $7$: $(10\backslash \%$ of Assignment Value$)$

Consider an experimental setup where charged particles $($electrons or protons$)$ are first accelerated by an electric field and then injected int magnetic field with a field strength of $0\mathrm{.}65$ T $.$

$-$ Part $($a$)\backslash (\backslash$checkmark $\backslash )$

What is the potential difference, in volts, required in the first part of the experiment to accelerate electrons to a speed of $\backslash (6\mathrm{.}1\backslash$times $10^\{7\}\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )?$

$\backslash [$

$\backslash$begin$\{$array$\}\{$l$\}$

V$=10593\backslash \backslash$

V$=1\mathrm{.}059\backslash$times $10^\{4\}$

$\backslash$end$\{$array$\}$

$\backslash ]$

$\backslash (\backslash$checkmark $\backslash )$ Correct!

Part $($b$).$

Find the radius of curvature, in meters, of the path of a proton accelerated through this same potential after the proton crosses into the r

$\backslash [$

r$\_\{\backslash$mathrm$\{$p$\}\}=$

$\backslash ]$ I II

O

DegreesRadians

$973$ Submission$($s$)$ Remaining

Hints: $\backslash (\backslash$underline$\{2\}\backslash )$ for a $\backslash (\backslash$underline$\{0\backslash \%\}\backslash )$ deduction. Hints remaining: $\backslash (\backslash$underline$\{0\}\backslash )$

$-$Make sure you understand why the path of the proton is curved in the region of magnetic field $-$ what happens to moving particles in a magnetic field?

$-$The proton gains kinetic energy from the electric field, just as the electron did, and its velocity determines the radius of curvature of its path in the magnetic field.

Feedback: $\backslash (0\backslash \%\backslash )$ deduction per feedback.

$-$ Part $($c$)\backslash (\backslash$boldsymbol$\{$V$\}\backslash )$

What is the ratio of the radii of curvature for a proton and an an electron traveling through this apparatus?

$\backslash [$

r$\_\{\backslash$mathrm$\{$p$\}\}/$ r$\_\{\backslash$mathrm$\{$e$\}\}=43\mathrm{.}00$

$\backslash ]$

$\backslash (\backslash$checkmark $\backslash )$ Correct!