A solid hemispherical uniform charged body having charge $Q$ is kept symmetrically along the $y$ -axis as…

A solid hemispherical uniform charged body having charge $Q$ is kept symmetrically along the $y$ -axis as shown in figure. The electric potential at a distance $d$ from the origin along the $x$ -axis at point $P$ will be
  1. $\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{d}$
  2. less than $\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{d}$
  3. more than $\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{d}$ and less than $\frac{2}{4 \pi \varepsilon_{0}} \frac{Q}{d}$
  4. more than $\frac{2}{4 \pi \varepsilon_{0}} \frac{Q}{d}$

Solution

Assuming sphere is complete then charge on it $=2 Q$
So potential at point $P$ due to this spherical charge $=\frac{1}{4 \pi \varepsilon_{0}} \frac{2 Q}{d}$
Hence potential due to hemisphere $=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{d}$
$\therefore \quad$ (a)

Asked in: JEE Mains - Electrostatics - Test 3

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