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This is about the electric field of a ring with radius r, at a distance z from center, along the axis of the ring. The ring carries a uniform line charge
λ
. We always say that the radial component of the field cancels out due to symmetry. Can somebody tell how to prove it mathematically (using cylindrical coordinate system only)?
dErad=−14πϵ0rλdθ(r2+z2)rˆ
Erad=−14πϵ0rλ(r2+z2)∫2π0rˆdθ
λ
. We always say that the radial component of the field cancels out due to symmetry. Can somebody tell how to prove it mathematically (using cylindrical coordinate system only)?
dErad=−14πϵ0rλdθ(r2+z2)rˆ
Erad=−14πϵ0rλ(r2+z2)∫2π0rˆdθ