Subject: Electromagnetics Consider a large flat horizontal sheet with thickness x and volume charge density p. This sheet is tangent to a sphere with radius R and volume charge density p0 as shown in the figure. Let A be the point at which the sheet is tangent to the sphere and let B be the point opposite to A on the top of the sheet. Show that the net upward electric field (from the sphere plus the sheet) at B is larger than at a if ? > 2p0/3. [Hint: A useful approximation is (1 + e) - 2 = 1 - 2E for e << 1]

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Subject: Electromagnetics

Consider a large flat horizontal sheet with thickness x and volume charge
density p. This sheet is tangent to a sphere with radius R and volume charge density p0 as shown
in the figure. Let A be the point at which the sheet is tangent to the sphere and let B be the point
opposite to A on the top of the sheet. Show that the net upward electric field (from the sphere plus
the sheet) at B is larger than at a if ? > 2p0/3. [Hint: A useful approximation is (1 + e) - 2 = 1 -
2E for e << 1]

Consider a large flat horizontal sheet with thickness x and volume charge
density p. This sheet is tangent to a sphere with radius R and volume charge density Po as shown
in the figure. Let A be the point at which the sheet is tangent to the sphere and let B be the point
opposite to A on the top of the sheet. Show that the net upward electric field (from the sphere plus
the sheet) at B is larger than at A if p > 2po/3. [Hint: A useful approximation is (1 + €)−² ≈ 1 −
2€ for € < 1]
X
A
B
R
Po
P
Transcribed Image Text:Consider a large flat horizontal sheet with thickness x and volume charge density p. This sheet is tangent to a sphere with radius R and volume charge density Po as shown in the figure. Let A be the point at which the sheet is tangent to the sphere and let B be the point opposite to A on the top of the sheet. Show that the net upward electric field (from the sphere plus the sheet) at B is larger than at A if p > 2po/3. [Hint: A useful approximation is (1 + €)−² ≈ 1 − 2€ for € < 1] X A B R Po P
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