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  • An electron enters with a velocity v = v0i into a cubical region (face parallel to coordinate planes) in which there are uniform electric and magnetic fields.

An electron enters with a velocity v = v_0i  into a cubical region (face parallel to coordinate planes) in which there are uniform electric and magnetic fields. The orbit of the electron is found to spiral down inside the cube in a plane parallel to the x-y plane. Suggest a configuration to fields E and B that can lead to it.

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The magnetic force makes a charged particle revolve in a uniform circular motion in the x-y plane, but the electric field increases the speed of the charged particle along the x-direction. This results in increasing the radius of the circular path and so, the moves in a spiral path.

Take the field present in the region to be B = B0 and electrons enters a cubical region with some velocity (faces parallel to coordinate planes). The force due to the Lorentz force on the electron is given by -

\overrightarrow{F}=-e\left ( v_{0}\widehat{i}\times B_{0}\widehat{k} \right )=ev_{0}B_{0}\widehat{j}

 

 This revolves the electron in an x-y plane.

With the increase in the radius of the circular path due to ‘e’ acceleration caused by the electric forceF = eE_0j, electron transverses on a spiral path.

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infoexpert24

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