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Q.

A long straight solid conductor of radius $5 c m$ carries a current of $2 A$ which is uniformly distributed over its circular cross-section. If the magnetic field induction at a distance of $3 c m$ from the axis of the conductor is $y \times 10^{- 6} T$ , then find the value of $y$ .

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answer is 5.

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Detailed Solution

current enclosed by the circular path, of radius $r (< R)$ is

$\begin{array}{l} I' = \frac{I}{π R^{2}} \times π r^{2} \\ ∮ \vec{B} \cdot d \vec{I} = μ_{0} I' \\ or B \times 2 π r = μ_{0} \frac{I r^{2}}{R^{2}} \\ ∴ B = \frac{10^{- 7} \times 2 \times 2 \times 0.03}{(0.05)^{2}} = 4.8 \times 10^{- 6} T \end{array}$

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