Magnetic field due to current element

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Question

The magnetic field (in Tesla) at point P due to a straight line segment AB of length 6 cm carrying a current of 5 A (See figure) is $p \times 10^{- 5} T$ . Find value of $p$ . $(μ_{o} = 4 π \times 10^{- 7} N - A^{- 2})$

Moderate

Solution

$\begin{array}{l} B = \frac{μ_{0}}{4 π} \frac{i}{r} (sinα + sinβ) \\ Here r = \sqrt{5^{2} - 3^{2}} = 4 cm \\ \Rightarrow α = β = 37^{\circ} \\ ∴ B = 10^{- 7} \times \frac{5}{4 \times 10^{- 2}} \times (\frac{3}{5} + \frac{3}{5}) = 1.5 \times 10^{- 5} T \end{array}$

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