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Electric potential due to continuous charge distribution(I) is considered one the most difficult concept.
18 Questions around this concept.
A thin disc of radius b=2a has a concentric hole of radius 'a' in it (see figure). It carries 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 :
The electric potential at the centre of two concentric half rings of radii $\mathrm{R}_1$ and $\mathrm{R}_{2,}$, having same linear charge density $\lambda$ is :
A spherical conducting shell of radius , centred at the origin, has a potential field with the zero references at infinity. The stored energy potential to
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Electric Potential due to uniformly charged ring
We want to find the electric potential at point P on the axis of the ring as of radius a, shown in the below figure
Take a small elemental arc of charge dq
Charge on an arc: dq
So
The potential at the center of the ring
(since x=0)
If x>>a
As x increases, V will decrease.
So the maximum potential is at the centre of the ring.
Electric Potential due to uniformly charged Disc-
We want to find the electric potential at point P on the axis of the disk of radius R, as shown in the below figure
Take a small elemental a ring of radius a having charge as dq
We can also write
The potential at the centre of the disc
(since x=0)
If x>>R
As |x| increases, V will decrease.
So the maximum potential is at the centre of the disc.
Electric Potential due to a finite uniform line of charge-
We want to find the potential due to a finite uniform line of positive charge at point P which is at a distance x from the rod on its perpendicular bisector, as shown in the below figure.
We get
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