Need help in PART B. kindly write the solution as well. Thanks
Let us calculate electric potential at P due to a charged ring of radius r. Point P is at a distance d from center of ring.
For a small charge element dr , potential dV at P is given by
where is linear charge density , i.e., charge density per unit length and
K = 1/(4) is Coulomb's constant
Electric potential V due to full ring is given as
since (2r) is the charge q in the ring , potential V due to ring at a axial distance d is written as
...........................(1)
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Now let us find the electric potential of a charged hollow cylinder at mid point of its axis. Let r be the radius of hollow cylinder and h is its height.
Let us fix origin of coordinate system at mid point of its axis as shown in figure .
Let us consider a ring of thickness ds at a distance s from origin
electric potential dV due to this ring is written using eqn.(1) as
where is surface charge density
Potential due to full hallow cylinder is given by
Above integration is performed using substitution s = r tan and we used the dfinition of surface charge density
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When h 0 , hallow cylinder becomes ring .
Let us consider the potential function
.........................(2)
when h 0 ,
Hence eqn.(2) is written as
...........................(3)
In above equation , argument of log function is by neglecting higher powers of h
Hence eqn.(3) will become
Above equation for potential is same as potential of ring at centre
Need help in PART B. kindly write the solution as well. Thanks Potential of a Charged...
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