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Physics · 2026 · 3 marks
CBSE 2026 · Region 2 · Set 1 · Q23
(a) An electric field E = E_0 i exists in a region of space. Draw three equipotential surfaces in the region. (b) Two point charges -q and +q are…
(a)
An electric field $\displaystyle \overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \hat{\mathrm{i}}$ exists in a region of space. Draw three equipotential surfaces in the region.
(b)
Two point charges -q and +q are located at points $\displaystyle (-\mathrm{a}, 0,0)$ and (a, $\displaystyle 0$, $\displaystyle 0$) respectively. Find the electrostatic potential at point $\displaystyle (\mathrm{x}, 0,0)$ where $\displaystyle \mathrm{x} \gg \mathrm{a}$.
Marking-scheme solution
(a)
Alternatively:
(b)
Potential at P due to $\displaystyle -q$ charge: $\displaystyle V_{-q}=-\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{q}{(x+a)}$
Potential at P due to $\displaystyle +q$ charge: $\displaystyle V_{+q}=\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{q}{(x-a)}$
Net potential at P: $\displaystyle V=V_{-q}+V_{+q}=\dfrac{-1}{4 \pi \varepsilon_{0}} \dfrac{q}{(x+a)}+\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{q}{(x-a)}$
$\displaystyle V=\dfrac{1}{4 \pi \varepsilon_{0}} \cdot \dfrac{q(2 a)}{\left(x^{2}-a^{2}\right)}$
For $\displaystyle x \gg a$: $\displaystyle V=\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{q(2 a)}{x^{2}}$
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