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Physics · 2023 · 3 marks
CBSE 2023 · Region 1 · Set 1 · Q26
(a) Twelve negative charges of same magnitude are equally spaced and fixed on the circumference of a circle of radius R as shown in Fig. (i).…
(a)
Twelve negative charges of same magnitude are equally spaced and fixed on the circumference of a circle of radius $\displaystyle R$ as shown in Fig. (i). Relative to potential being zero at infinity, find the electric potential and electric field at the centre C of the circle.
(b)
If the charges are unequally spaced and fixed on an arc of $\displaystyle 120^{\circ}$ of radius $\displaystyle R$ as shown in Fig. (ii), find electric potential at the centre $\displaystyle C$.
(i)
(ii)
Marking-scheme solution
(a)
Electric potential due to point charge
\[\mathrm{V}=\frac{k \mathrm{q}}{R}
\]
Value of each charge \(\displaystyle =-\mathrm{q}\), Total charge \(\displaystyle =-12 \mathrm{q}\)
Total potential \(\displaystyle \mathrm{V}=\frac{k(-12 \mathrm{q})}{R}\)
\[\mathrm{V}=\frac{-12 k \mathrm{q}}{R}=\frac{-12 \mathrm{q}}{4 \pi \epsilon_{0} R}
\]
By symmetry the resultant of all electric field vectors becomes zero.
So electric field is zero.
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CBSE Class 12 Physics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.