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 ​ = 2 π a μ 0 ​ I ​ 2 B m a x ​ ​ = 4 π a μ 0 ​ I ​ ​ It can be obtained inside as well as outside the wire For inside, ​ 4 π a μ 0 ​ I ​ = 2 π a 2 μ 0 ​ Ir ​ ⇒ r = 2 a ​ ​ For outside ​ 4 π a μ 0 ​ I ​ = 2 π r μ 0 ​ I ​ ⇒ r = 2 a ​ Correct answer [ 2 a ​ , 2 a ]

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