Consider a long straight wire of a circular cross-section (radius a) carrying a steady current . 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

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Solution

Q.
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 [2025]

1 $[\frac{a}{4}, \frac{a}{2}]$

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

3 $[\frac{a}{2}, 3 a]$

4 $[\frac{a}{4}, 2 a]$

Ans.
(2)

Maximum possible magnetic field on the surface

$B_{\max} = \frac{μ_{0} I}{2 π a} \Rightarrow \frac{B_{\max}}{2} = \frac{μ_{0} I}{4 π a}$

It can be obtained inside as well as outside the wire.

For inside, $\frac{μ_{0} I}{4 π a} = \frac{μ_{0} I r}{2 π a^{2}} \Rightarrow r = \frac{a}{2}$

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

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

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