Question

Using the equations listed on the side, prove that the amount of deflection is given by the equation below:

3. prove that the amount of deflection is given by 1 D 2 Y A Equa Hons Vx.

Answer 1

horizontal velocity imparted=sqrt(2*q*Va/m)

time taken to reach the other end=Dx/speed

=Td=Dx/Vx

time taken to travel distance X=Tf=X/Vx

force along y axis=charge*electric field

=charge*potential difference/distance

=q*Vd/Dy

then acceleration=force/mass

=q*Vd/(Dy*m)

velocity along y axis=acceleration*time

=q*Vd*Td/(Dy*m)

deflection along y axis=velocity*Tf

=q*Vd*Td*tf/(Dy*m)

=q*Vd*Dx*X/(Vx^2*Dy*m)

=q*Vd*Dx*X/(2*q*Va*Dy*m/m)

=Vd*Dx*X/(2*Dy*Va)

hence proved.