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 \[{{B}_{c}}=\frac{{{\mu }_{0}}nI}{2r}\] ...(i) Magnetic induction on the axial line of a circular coil at a distance x from the centre is \[{{B}_{a}}=\frac{{{\mu }_{0}}n\,{{r}^{2}}I}{2{{({{r}^{2}}\times {{x}^{2}})}^{3/2}}}\] 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 \[\frac{{{B}_{c}}}{{{B}_{a}}}=\frac{2\sqrt{2}}{1}\]
You need to login to perform this action.
You will be redirected in
3 sec
