Q108 / 180 · AIIMS 2019 (26 May) · Physics

Find force per unit length at $P$. Figure

  • A
    $10^{-4} \mathrm{~m}$
  • Correct answer
    B
    $10^{-4} \mathrm{~N} \mathrm{~m}^{-1}$
  • C
    $10^{-4} \mathrm{~N} \mathrm{~m}^{-1}$
  • D
    $0.3 \mathrm{~N} \mathrm{~m}^{-1}$

Solution

Let length of wire element at $P$ is $d$. Magnetic field at $P$, $\begin{aligned} & B=\frac{\mu_0 i}{4 \pi r}+0+\frac{\mu_0 i}{4 \pi r} \\ & B=\frac{\mu_0 \times 5}{4 \pi \times 5 \times 10^{-2}} \times 2=\frac{\mu_0 \times 200}{4 \pi} \\ & B=2 \times 10^{-5} \mathrm{~T} \\ & F=i B d l \Rightarrow \frac{F}{d l}=i B=5 \times 2 \times 10^{-5}=10^{-4} \mathrm{Nm}^{-1}\end{aligned}$

Hence, the correct answer is option: 'B'.

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