Match List I (current configuration, see figure) with List II (magnetic field at point $O$).
List II:
I. $B_0=\dfrac{\mu_0I}{4\pi r}[\pi+2]$
II. $B_0=\dfrac{\mu_0}{4}\dfrac Ir$
III. $B_0=\dfrac{\mu_0I}{2\pi r}[\pi-1]$
IV. $B_0=\dfrac{\mu_0I}{4\pi r}[\pi+1]$
Choose the correct answer from the options given below:
Answer: (C) A-III, B-I, C-IV, D-II
- A: the circular loop gives $\dfrac{\mu_0I}{2r}$ and the long straight wire gives $\dfrac{\mu_0I}{2\pi r}$ in the opposite direction: $B=\dfrac{\mu_0I}{2\pi r}(\pi-1)$ → III
- B: two semi-infinite wires, each $\dfrac{\mu_0I}{4\pi r}$, plus a semicircle $\dfrac{\mu_0I}{4r}$, all in the same sense: $\dfrac{\mu_0I}{4\pi r}(\pi+2)$ → I
- C: the wire leaving along a line through $O$ gives nothing; semicircle $\dfrac{\mu_0I}{4r}$ plus one semi-infinite wire $\dfrac{\mu_0I}{4\pi r}$: $\dfrac{\mu_0I}{4\pi r}(\pi+1)$ → IV
- D: the straight parts pass through the line of $O$ and give nothing; only the semicircle: $\dfrac{\mu_0I}{4r}$ → II
Solution by Sreeraj P, M.Sc Physics