We have to find the distance along the charged disk of radius R where the electric field strength is equal to one-half of the value of the field at the surface of the disk at the centre.

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We recall that the electric field strength at a distance z along the axis from the centre of a charged disk of radius R and surface charge density is given by the expression

From this we note that the electric field strength at the centre of the disk is

Therefore, the distance z along the axis where the strength of the electric field will be one-half of its value at the centre will be given by the equation

or

We therefore have the condition that