A) 4 : 1
B) 1 : 4
C) 2 : 1
D) 1 : 2
Correct Answer: A
Solution :
\[\frac{{{B}_{1}}}{{{B}_{2}}}\,\,=\,\,\frac{{{I}_{1}}}{{{I}_{2}}}\,\times \,\frac{{{r}_{2}}}{{{r}_{1}}}\] \[\,\,\frac{{{I}_{1}}}{{{I}_{2}}}\,\,=\,\frac{V/{{R}_{1}}}{V/{{R}_{2}}}\,\,\,=\,\,\frac{{{R}_{2}}}{{{R}_{1}}}\,\,=\,\,\,\frac{\rho {{\ell }_{2}}/A}{\rho {{\ell }_{1}}/A}\,\,=\,\,\frac{{{\ell }_{2}}}{{{\ell }_{1}}}\] \[=\,\,\,\frac{2{{r}_{2}}}{2\pi {{r}_{1}}}\,\,=\,\,\frac{{{r}_{2}}}{{{r}_{1}}}\] \[\therefore \,\,\,\frac{{{B}_{1}}}{{{B}_{2}}}\,\,=\,\,\frac{{{r}_{2}}}{{{r}_{1}}}\,\,\times \,\,\frac{{{r}_{2}}}{{{r}_{1}}}\,\,=\,\,{{\left( \frac{40}{20} \right)}^{2}}\,\,=\,\,4\]
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