A conducting sphere with radius R and electric charge Q > 0 is cut into a large number of thin circular rings of radius r = R sin θ, each having a charge dQ = σ (2πr ds). Each ring produces a vertical electric field dE = dEzˆkdEzˆ dEzˆk at point P.

Contexts in source publication

Context 1

... Without loss of generality, take Q > 0 and the z-axis along the line from the center, at x = y = z = 0, to point P, at x = y = 0 and z = R, as seen in Fig. 1, below. On treating the spherical charge distribution as a collection of horizontal circular rings with radius r, varying from 0 to R, and variable charge dQ = σ dA = σ (2π r ds), where ds = R dθ is the width of each ring, θ being the polar angle (in spherical coordinates), we begin deriving the electric field dE created in P by the ...

Context 2

... radius r, varying from 0 to R, and variable charge dQ = σ dA = σ (2π r ds), where ds = R dθ is the width of each ring, θ being the polar angle (in spherical coordinates), we begin deriving the electric field dE created in P by the charged ring centered at point (0, 0, z), with −R ≤ z < +R, which lies at a distance R − z from P, as indicated in Fig. 1. The azimuthal symmetry of the charge distribution guarantees that the field in P must point along the z-axis direction, so dE = dE z ˆ k, wherêwherê k is the unit-vector for the z-axis ...