Subject: Applied Physics 2

Topic: Motion Of Charged Particles In Electric And Magnetic Fields

Difficulty: Low

Measurement of phase difference.

An elliptical trace is obtained when an electron beam is acted upon simultaneously by two perpendicular sinusoidal signals As shown in figure.

The phase difference is given by Sinϕ =A/B
ϕ =$sin^{-1}$⁡(A/B)

 For equal voltage (a= b) and zero phase difference (ϕ =0), equation (3) reduces to y=x, which describes a straight line with a positive slope.


For equal voltage (a=b) and signal out of phase (ϕ = 180°) , in this case equation (3) becomes y = -x, describing a straight line with a negative slope.


 For unequal voltages a> b and ϕ = 90°


Equation (3) reduces to  x^2/a^2 +y^2/b^2 =1, which is equation of ellipse.


For equal voltage (a=b) and ϕ= 90°, Equation (3) becomes x^2 +y^2 = a^2 equation of circle of radius a.