The electric field of a uniformly charged disk is a fundamental problem in electrostatics, frequently encountered in physics. A charged disk generates an electric field that varies with distance from its surface, and its distribution of charge plays a crucial role in determining the field's characteristics. The field is typically analyzed in the plane perpendicular to the disk's surface, with special attention to the axis passing through its centre.
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Let us take a disk of radius R with a uniform positive surface charge density (charge per unit area)
From the figure, we can see that we have taken a typical ring that has charge
If we integrate from 0 to
Here, '
As this disc is symmetric to the x -axis, the field in the rest of the component is zero i.e.,
Special case -
1) When
2) When
Example 1: A thin disc of radius b=2a has a concentric hole of radius 'a' in it (see figure). It carries a uniform surface charge on it. If the electric field on its axis at height' h ' (h<<a) from its centre is given as 'Ch' then value of 'C' is :
3)
Solution:
As we discussed in
Uniformly charged disc -
- wherein
Electric Field due to complete disc
Similarly, the electric field due to disc
Now
Hence
Example 2: What will be the electric field due to a uniformly charged disc At a distance
4)0
Solution:
As we learned
Uniformly charged disc -
wherein
i.e. Point situated near the disc it behaves as an infinite sheet of charge.
Example 3 The surface charge density of a thin charged disc of radius R is The value of the electric field at the centre of the disc is
1)reduces by
2)reduces by
3)reduces by
4)reduces by
Solution:
Electric field intensity at the centre of the disc
Electric field along the axis at any distance
From question,
So reduction in the value of electric field
Example 4:Find out the surface charge density at the intersection of point
1)
2)
3)
4)
Solution:
Electric field due to uniformly charged rod-
Electric field due to uniformly charged disk-
To compute the electric field at a point along the axis of a uniformly charged disk, the disk is treated as a series of infinitesimal rings of charge. Each ring contributes to the net electric field, with its components integrated to find the total field. For a point close to the disk, the field behaves like that of a charged plane, while at far distances, it resembles the field of a point charge. The formula derived depends on the radius of the disk, surface charge density, and the distance from the point of interest to the disk’s centre.
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