All Problems

Conductors and Dielectrics in an Electric Field

Problem 3.62

A thin wire ring of radius RR carries a charge qq. The ring is oriented parallel to an infinite conducting plane and is separated by a distance ll from it. Find: (a) the surface charge density at the point of the plane symmetrical with respect to the ring; (b) the strength and the potential of the electric field at the centre of the ring.

Reveal Answer
3.62. (a) σ=lq2π(l2+R2)3/2\sigma=\frac{l q}{2 \pi\left(l^{2}+R^{2}\right)^{3 / 2}} (b) E=14πε0q4l2[1+1/4(R/l)2]3/2E=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{4 l^{2}\left[1+1 / 4(R / l)^{2}\right]^{3 / 2}}, φ=14πε0qR(1−11+4(l/R)2)\varphi=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{R}\left(1-\frac{1}{\sqrt{1+4(l / R)^{2}}}\right)
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