A) \[1:\sqrt{2}\]
B) \[1:2\sqrt{2}\]
C) \[2\sqrt{2}:1\]
D) \[\sqrt{2}:1\]
Correct Answer: C
Solution :
Magnetic induction at the centre of the coil of radius r is \[{{B}_{c}}=\frac{{{\mu }_{0}}nI}{2\,r}\] ... (i) Magnetic induction on the axial line of a circular coil at a distance x from the centre is \[{{B}_{a}}=\frac{{{\mu }_{0}}n{{r}^{2}}I}{2{{({{r}^{2}}+{{x}^{2}})}^{3/2}}}\] Given \[x=r\] \[\therefore \] \[{{B}_{a}}=\frac{{{\mu }_{0}}n{{r}^{2}}I}{2{{(2{{r}^{2}})}^{3/2}}}\] ?. (ii) From Eqs. (i) and (ii), we get \[\frac{{{B}_{c}}}{{{B}_{a}}}=\frac{2\sqrt{2}}{1}\]
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