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A hemispherical earth plate is buried into the earth. Find the potential difference between the feet of a man standing on ground as shown in figure. Current through earth plate is I. Conductivity of earth is [δ=103π,I=1A](up to two decimal places)

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Solution

j=σE
Assuming that the current density is uniform in all directions ,
i2πr2=σE
where, 2πr2 is the surface area of the hemisphere
E=i2πr2σΔV=E.dr=32i dr2πr2δ
ΔV=i2πδ(1r)32ΔV=12×π×π×103×16=10312π2

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