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a$.$Electric and magnetic $(60$ T in the x$-$direction$)$ fields are adjusted such that an electron emerges with a constant velocity of $51\mathrm{.}2103$ m$/$s$.($i$)$ Define a coordinate system and sketch the situation of the velocity, E$-$ and B$-$fields. You will have to make some assumptions. $($ii$)$ What is the strength of the electric field?

The electron continues moving and enters a new region where a different magnetic field forces the electron to follow a helical trajectory. The electron enters the new magnetic field region at an angle of $30\mathrm{.}0$ relative to the incoming velocity and has a cyclotron period of $3$ s$.$

b$.$ What is the $($iii$)$ strength of the new magnetic field, $($iv$)$ radius of rotation and the $($v$)$ pitch of the helical trajectory?

c$.$Describe the trajectory of the electron. a$.$ Electric and magnetic $(\backslash (60\backslash$mu $\backslash$mathrm$\{$~T$\}\backslash )$ in the x $-$direction$)$ fields are adjusted such that an electron emerges with a constant velocity of $\backslash (51\mathrm{.}2\backslash$times $10^\{3\}\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).($i$)$ Define a coordinate system and sketch the situation of the velocity, E$-$ and B$-$fields. You will have to make some assumptions. $($ii$)$ What is the strength of the electric field?

The electron continues moving and enters a new region where a different magnetic field forces the electron to follow a helical trajectory. The electron enters the new magnetic field region at an angle of $\backslash (30\mathrm{.}0^\{\backslash$circ$\}\backslash )$ relative to the incoming velocity and has a cyclotron period of $\backslash (3\backslash$mu $\backslash$mathrm$\{$~s$\}\backslash ).$

b$.$ What is the $($iii$)$ strength of the new magnetic field, $($iv$)$ radius of rotation and the $(\backslash ($ v $\backslash ))$ pitch of the helical trajectory?

c$.$ Describe the trajectory of the electron

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