\(B=\frac{\mu_{0} i}{4 \pi r}+0+\frac{\mu_{0} i}{4 \pi r}\)
\(=\frac{\mu_{0} \times 5}{4 \pi \times 5 \times 10^{-2}} \times 2\)
\(=\frac{\mu_{0}}{4 \pi} \times 200\)
\(=2 \times 10^{-5} T\)
Consider the length of wire element at \(P\) is \(dl\).
The force per unit length at \(P\) is,
\(F=i B d l\)
\(\frac{F}{d l}=i B\)
\(=5 \times 2 \times 10^{-5}\)
\(=10^{-4} N / m\)
$(i)$ | $(ii)$ | $(iii)$ |
(A) $\frac{{{\mu _0}i}}{2r}$ $\odot$ | (A) $\frac{{{\mu _0}}}{{2\pi }}\frac{i}{r}(\pi - 2)$ | (A) $\frac{{{\mu _0}}}{{2r}}\frac{{2i}}{r}(\pi + 1)$ $\otimes$ |
(B) $\frac{{{\mu _0}i}}{{2r}}$ $\otimes$ | (B) $\frac{{{\mu _0}i}}{{4\pi }}.\frac{i}{r}(\pi + 2)$ $\otimes$ | (B) $\frac{{{\mu _0}i}}{{4r}}.\frac{{2i}}{r}(\pi - 1) \otimes $ |
(C) $\frac{{{3\mu _0}i}}{{8r}}$ $\otimes$ | (C) $\frac{{{\mu _0}i}}{4r}$ $\otimes$ | (C) $Zero$ |
(D) $\frac{{{3\mu _0}i}} {{8r}}$ $\odot$ | (D) $\frac{{{\mu _0}i}}{4r}$ $\odot$ | (D) $Infinite$ |