A length of wire carries a steady current. It is bent first to form a circular plane coil of one tur

Question

A length of wire carries a steady current. It is bent first to form a circular plane coil of one turn. The same length is now bent more sharply to give a double loop of a smaller radius the magnetic field at the center caused by the same current is\

Professor PC Thomas Classes · Answer

Case 1\ $\mathrm{n}=1$\ $\mathrm{r}=\mathrm{r}$\ $\mathrm{B}=\frac{\mu_{0} \mathrm{nI}}{2 \mathrm{r}}=\frac{\mu_{0} 	imes 1 	imes \mathrm{I}}{2 \mathrm{r}}$\ Case II\ $\mathrm{n}=2$\ $\mathrm{r}^{\prime}=\frac{\mathrm{r}}{2}$\ $\mathrm{B}^{\prime}=\frac{\mu_{0} \mathrm{nI}}{2 \mathrm{r}^{\prime}}=\frac{\mu_{0} 2 	imes 2 	imes \mathrm{I}}{2}$ $$ \begin{equation*} \frac{\mathrm{B}^{\prime}}{\mathrm{B}}= 	ag{1} \end{equation*} $$