An electron moves to the right at a constant speed of 2.5 10^6 m/s until it ente

Question

An electron moves to the right at a constant speed of 2.5 10^6 m/s until it enters a uniform magnetic field that is directed out of the page with a magnitude of 0.10 T. With the magnetic field alone, the electron will be deflected and undertake a semi-circular trajectory until it exits the field.

Design an apparatus that will create an electric field that allows the electron to pass through the magnetic field undeflected; that is, it moves in a straight line at a constant speed through the magnetic field. Show any calculations, add a drawing of the apparatus to the diagram below, show the resulting trajectory of the electron, and specify all design parameters for your apparatus: what is it made out of, how big is it, what are all the relevant dimensions, is a power supply required, and if so what voltage or current is needed, etc.

F=qv*B

Explanation / Answer

we will create an electrci field such that its force will cancel the magnetic force ;

when electron moves to the right , the magnetic force will be upwards ,

so we will design electric field so that force is downwards , or positve field is upwards ,  

since there is no deflection , the electrons path will be strt line to the right ,the forces balance .

e E = e v B ;

or E = v B ;

electric field = 2.5 e 6 * 0.1 = 2.5 e 5 N / C .

this will be the strength of the electrci field , one needs a capacitor to set up this field ;

say the distance betewwn the plates is 3 mm , then a potential = V = Ed should be set up between the plates ,

say for d = 3mm ;

potenrial difference = 2.5 e 5   * ( 3 e -3 ) = 750 V , between the plates ,

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