First slide

Force on a current carrying wire placed in a magnetic field

Question

A straight conductor of length 2m is carrying a current of 10 A. P is a paint at a distance of $2 \sqrt{3} m$ from end A as shown in figure. then magnetic induction at P is

Moderate

A

$4 \sqrt{3} μT$
B

$\frac{1}{4} μT$
C

$\frac{1}{4 \sqrt{3}} μT$
D

$2 \sqrt{3} μT$

Solution

$\begin{array}{l} B_{P} = \frac{μ_{o} i}{4 πd} sinθ \\ tanθ = \frac{2}{2 \sqrt{3}} = \frac{1}{\sqrt{3}} \Rightarrow θ = 30^{o} \\ ∴ sinθ = \frac{1}{2} \\ B_{P} = 10^{- 7} \times \frac{10}{2 \sqrt{3}} \times \frac{1}{2} T = \frac{1}{4 \sqrt{3}} μT . \end{array}$

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