$A$ circular coil of wire of radius $r$ has $n$ turns and carries a current $I$. The magnetic induction $B$ at a point on the axis of the coil at a distance $\sqrt{3} r$ from its centre is
- A$\frac{\mu_0 n I}{8 r}$
- B$\frac{\mu_0 n I}{16 r}$
- C$\frac{\mu_0 n I}{4 r}$
- D$\frac{\mu_0 n I}{32 r}$
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$A$ coil having $N$ turns carries a current $I$ as shown in the figure. The magnetic field intensity at point $P$ is
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View Solution$A$ circular arc of wire of radius of curvature $r$ subtends an angle of $\frac{\pi}{5}$ radian at its centre. If current $i$ is flowing in it, then the magnetic induction at its centre is ($\mu_0$ = permeability of free space).
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The magnetic field at point $O$ for the given circuits is provided. Which of the following is correct?
$(i)$ $(ii)$ $(iii)$ $(A). \frac{\mu_0 i}{2r} \odot$ $(A). \frac{\mu_0}{2\pi} \frac{i}{r}(\pi - 2)$ $(A). \frac{\mu_0}{2r} \frac{2i}{r}(\pi + 1) \otimes$ $(B). \frac{\mu_0 i}{2r} \otimes$ $(B). \frac{\mu_0 i}{4\pi} \frac{i}{r}(\pi + 2) \otimes$ $(B). \frac{\mu_0 i}{4r} \frac{2i}{r}(\pi - 1) \otimes$ $(C). \frac{3\mu_0 i}{8r} \otimes$ $(C). \frac{\mu_0 i}{4r} \otimes$ $(C). \text{Zero}$ $(D). \frac{3\mu_0 i}{8r} \odot$ $(D). \frac{\mu_0 i}{4r} \odot$ $(D). \text{Infinite}$
| $(i)$ | $(ii)$ | $(iii)$ |
|---|---|---|
| $(A). \frac{\mu_0 i}{2r} \odot$ | $(A). \frac{\mu_0}{2\pi} \frac{i}{r}(\pi - 2)$ | $(A). \frac{\mu_0}{2r} \frac{2i}{r}(\pi + 1) \otimes$ |
| $(B). \frac{\mu_0 i}{2r} \otimes$ | $(B). \frac{\mu_0 i}{4\pi} \frac{i}{r}(\pi + 2) \otimes$ | $(B). \frac{\mu_0 i}{4r} \frac{2i}{r}(\pi - 1) \otimes$ |
| $(C). \frac{3\mu_0 i}{8r} \otimes$ | $(C). \frac{\mu_0 i}{4r} \otimes$ | $(C). \text{Zero}$ |
| $(D). \frac{3\mu_0 i}{8r} \odot$ | $(D). \frac{\mu_0 i}{4r} \odot$ | $(D). \text{Infinite}$ |
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