I need i j k and unit In the figure, an electron accelerated from rest through p

Question

I need i j k and unit

In the figure, an electron accelerated from rest through potential difference V1=0.984 kV enters the gap between two parallel plates having separation d = 24.0 mm and potential difference V2= 198 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap? I need i j k and unit

Explanation / Answer

Electric field

E=V2/d =198/(24*10^-3)=8250 V/m

Magnetic force =force due to electric field

qvB=qE

=>B=E/v

By conservation of energy

(1/2)mv2=qV1

=>v=sqrt[2qV1/m]=sqrt[2*1.6*10^-19*984/9.11*10^-31]

v=1.86*10^7 m/s

so

B=8250/(1.86*107) =4.44*10-4 T or 0.444 mT

In Unit Vector notation

B=-(0.444 mT) k

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