Question

An electron beam is deflected in a given field. How will you detect whether the given field is a uniform magnetic field or a uniform electric field.

Answer 1

Dear Student,

For a uniform electric field

ma=qE or a=qE/m

if E is in direction of electron beam there will be no deflection
if E is perpendicular to electron beam

$S=ut+0.5a{t}^2\Rightarrow ut+\frac{qE}{2m}whereq=-1.6\times {10}^{-19}C$
if the field is uniform acceleration will be constant


For a uniform magnetic

$$\begin{gathered} ma=q\left(v\times B\right) \\ or,a=\frac{qvB\sin \theta }{m}magnitudewise \\ but\sin cedirectionofvelocitychangessodoesdoesthatofacceleration. \\ Ifthefieldisperpendiculartothebeam \\ thebeamwillbedeflectedinacirculartrajectory \\ butforauniformfieldmagnitudeofaccelerationwillbecons\tan t. \end{gathered}$$

Regards.