First slide

Electric field

Question

Figure shows a uniformly charged hemisphere of radius R. It has a volume charge density $ρ$ . If the electric field at a point 2R, above its center is E, then what is the electric field at the point 2Rbelow its center?

Moderate

A

$ρ R / 6 ε_{0} + E$
B

$ρ R / 12 ε_{0} - E$
C

$- ρ R / 6 ε_{n} + E$
D

$ρ R / 12 ε_{0} + E$

Solution

Let us complete the sphere. Electric field due to lower part at A is equal to electric field due to upper Part at B = E (given) Electric field due to lower part at B = electric fleld due to full sphere - electric field due to upper Part
$\begin{array}{l} = \frac{k Q}{(2 R)^{2}} - E \\ = \frac{1}{4 π ε_{0}} \frac{ρ (4 / 3) π R^{3}}{4 R^{2}} - E \\ = \frac{ρ R}{12 ε_{0}} - E \end{array}$

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