Q.
At what distance along the central axis of a uniformly charged plastic disc of radius R is the magnitude of the electric field equal to one-half the magnitude of the field at the centre of the surface of the disc?
At a point on the axis of uniformly charged disc at a distance x above the centre of the disc, the magnitude of the electric fieid is
E = 2ε0σ[1−x2+R2x]
but Ec=2ε0σsuchthat,EcE=21
Then, 1−x2+R2x=21
or x2+R2x=21
Squaring both sides and multiplying by x2+R2 to obtain x2=4x2+4R2
Thus, x2=3R2
x = 3R