Question

A disk of radius 2.6 cm has a surface charge density of 6.0 µC/m2 on its upper face. What is the magnitude of the electric field produced by the disk at a point on its central axis at distance z = 18 cm from the disk?

Answer 1

Electric field on the axis of a ring of total charge Q is given by

...........................(1)

As all components along the perpendicular direction gets cancelled out.

Here,

Electric field due to uniformly charge disk on its axis at a distance ' z ' from the plane of the disk :

The surface charge density () of the disk is given by

Where, Q is total charge on the disk and R is radius of the disk.

  

Let us consider an elemental ring of width ' ' at a distance ' ' from the on the disk.

The differential area of this ring will be

  

So, the charge on the ring will be

Now, using equation (1) we can write the field produced by this ring along the z - axis as

  

So, the total field due to the whole disk will be

  

  

  

or,   

or,    ....................................(2)

According to the question,

  

Putting these values in equation (2), we get

  

  

  

Hence, the disk will produce an electric field of 3485.086 N/C at a distance 18 cm from the disk .

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