Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the w

Question

Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire's cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be

TestHub · Accepted Answer

Maximum possible magnetic field is at the surface
$B_{m a x} = \frac{μ _{0} I}{2 π a} \frac{B _{m a x}}{2} = \frac{μ _{0} I}{4 π a}$

It can be obtained inside as well as outside the wire For inside,
$\frac{μ _{0} I}{4 π a} = \frac{μ _{0} Ir}{2 π a ^{2}} \Rightarrow r = \frac{a}{2}$

For outside
$\frac{μ _{0} I}{4 π a} = \frac{μ _{0} I}{2 π r} \Rightarrow r = 2 a$

Correct answer $[\frac{a}{2}, 2 a]$

Physics - Magnetic Effect of Current Question with Solution | TestHub

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