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Physics · 2026 · 2 marks
CBSE 2026 · Region 1 · Set 1 · Q19
A wire of length L is bent round into (i) a square coil having N turns and (ii) a circular coil having N turns. The coil in both cases is free to…
A wire of length L is bent round into (i) a square coil having N turns and
(ii)
a circular coil having N turns. The coil in both cases is free to turn about a vertical axis coinciding with the plane of the coil, in a uniform, horizontal magnetic field and carry the same currents. Find the ratio of the maximum value of the torque acting on the square coil to that on the circular coil.
Marking-scheme solution
Side of square $\displaystyle \mathrm{a}=\dfrac{\mathrm{L}}{4 \mathrm{~N}}$ and radius of circular coil $\displaystyle \mathrm{r}=\dfrac{\mathrm{L}}{2 \pi \mathrm{~N}}$
$\displaystyle \tau=\mathrm{NIBA}$
$\displaystyle \dfrac{\tau_{1}}{\tau_{2}}=\dfrac{\mathrm{NIBA}_{1}}{\mathrm{NIBA}_{2}}$
$\displaystyle \dfrac{\tau_{1}}{\tau_{2}}=\dfrac{\mathrm{A}_{1}}{\mathrm{A}_{2}}$
$\displaystyle \dfrac{\tau_{1}}{\tau_{2}}=\dfrac{\left(\dfrac{\mathrm{L}}{4 \mathrm{~N}}\right)^{2}}{\pi\left(\dfrac{\mathrm{L}}{2 \pi \mathrm{~N}}\right)^{2}}$
$\displaystyle \dfrac{\tau_{1}}{\tau_{2}}=\dfrac{\pi}{4}$
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CBSE Class 12 Physics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.