question_answer

A long straight wire of radius a carries a steady current i. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at\[2a/\sqrt{3}\]and\[2a\sqrt{3}\]is       AIEEE  Solved  Paper-2007

A)  \[a/\sqrt{3}\]                                   

B)  4            

C)         1            

D)         \[a\sqrt{3}\]

Correct Answer: C

Solution :

Current density \[k\ge 1/2\] From Ampere's circuital law \[-1/2\le k\le 1/2\] For \[k\le 1/2\] \[2x+3y+z=1\] \[x+3y+2z=2\] \[cos\text{ }\alpha \] At \[1/\sqrt{3}\]               \[1/\sqrt{2}\] For\[{{x}^{2}}={{y}^{2}}+xy\frac{dy}{dx}\]\[{{x}^{2}}={{y}^{2}}+3xy\frac{dy}{dx}\]\[{{y}^{2}}={{x}^{2}}+2xy\frac{dy}{dx}\]\[{{y}^{2}}={{x}^{2}}-2xy\frac{dy}{dx}\] At\[{{p}^{2}}+{{q}^{2}}=1,\]                        \[(p+q)\] So,          \[\frac{1}{2}\]