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 2007]

A)       \[a/\sqrt{3}\]

B) 4         

C) 1

D) \[a\sqrt{3}\]    

Correct Answer: C

Solution :

[c] 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,       \[\frac{1}{2}\]