Question

Find the magnetic induction at point O, if the current carrying wire is in the shape shown in the figure.

• A. $\frac{{\mu }_0\text{I}}{5\pi \text{r}}\left[\frac{3\pi }{2}+1\right]⨀$
• B. $\frac{{\mu }_0\text{I}}{3\pi \text{r}}\left[\frac{4\pi }{3}+1\right]⨀$
• C. $\frac{{\mu }_0\text{I}}{2\pi \text{r}}\left[\frac{3\pi }{4}+1\right]⨀$
• D. $\frac{{\mu }_0\text{I}}{4\pi \text{r}}\left[\frac{3\pi }{2}+1\right]⨀$

Answer 1

Answer: (D)

$B_1=0\text{,}$
$B_2=\frac{{\mu }_0}{4\pi }\frac{\text{I}}{\text{r}}\times \frac{3\pi }{2}⨀$ ,
$B_3=\frac{{\mu }_0}{4\pi }\frac{\text{I}}{\text{r}}⨀$
$B=B_2+B_3=\frac{{\mu }_0\text{I}}{4\pi \text{r}}\left[\frac{3\pi }{2}+1\right]⨀$