Ampere's circuital law

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Question

A long straight current carrying conductor has a radius R. Magnetic field at a distance 2R from the axis of the conductor is $10 μT$ . Then magnetic field at a distance R/2 from the axis of the conductor is

Moderate

Solution

$\frac{μ_{0} i}{2 π (2 R)} = B \Rightarrow μ_{0} i = 4 πRB = 4 πR x 10 = 40 πR unit$
$∴$ At a distance R/2 from the axis of the conductor
$B' = \frac{μ_{0}}{2} \frac{i}{{πR}^{2}} . \frac{R}{2} = \frac{1}{4} (μ_{0} i) . \frac{1}{πR} = \frac{1}{4} x 40 πR x \frac{1}{πR} = 10 μT$

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