Question 278: Magnetism and Matter

Question

Two circular coils $$P$$ and $$Q$$ of 100 turns each have same radius of $$\pi \mathrm{~cm}$$. The currents in $$P$$ and $$R$$ are $$1 A$$ and $$2 A$$ respectively. $$P$$ and $$Q$$ are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is $$\sqrt{x} ~m T$$, where $$x=$$ __________.
[Use $$\mu_0=4 \pi 	imes 10^{-7} \mathrm{~TmA}^{-1}$$]

Accepted Answer

$$\begin{aligned}
& \mathrm{B}_{\mathrm{P}}=\frac{\mu_0 \mathrm{Ni}_1}{2 \mathrm{r}}=\frac{\mu_0 	imes 1 	imes 100}{2 \pi}=2 	imes 10^{-3} \mathrm{~T} \
& \mathrm{~B}_{\mathrm{Q}}=\frac{\mu_0 \mathrm{Ni}_2}{2 \mathrm{r}}=\frac{\mu_0 	imes 2 	imes 100}{2 \pi}=4 	imes 10^{-3} \mathrm{~T} \
& \mathrm{~B}_{	ext {net }}=\sqrt{\mathrm{B}_{\mathrm{P}}^2+\mathrm{B}_{\mathrm{Q}}^2} \
& =\sqrt{20} \mathrm{mT} \
& \mathrm{x}=20
\end{aligned}$$

Magnetism and Matter

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