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(A) The magnetic field $B$ produced by a long straight current-carrying wire at a distance $r$ is given by the formula:$B = \frac{\mu_0 i}{2 \pi r}$Fr

Vedclass · Accepted Answer

$(a)$ $2 \ T, (b) \frac{1}{2} \ T, (c) \frac{1}{3} \ T$

Vedclass · Answer

(A) The magnetic field $B$ produced by a long straight current-carrying wire at a distance $r$ is given by the formula:$B = \frac{\mu_0 i}{2 \pi r}$From this expression,we can see that $B \propto \frac{1}{r}$.Given that at distance $r$,$B = 1 \ T$.$(a)$ At distance $\frac{r}{2}$:$B_{\frac{r}{2}} = B 	imes \frac{r}{\frac{r}{2}} = 1 	imes 2 = 2 \ T$.$(b)$ At distance $2r$:$B_{2r} = B 	imes \frac{r}{2r} = 1 	imes \frac{1}{2} = \frac{1}{2} \ T$.$(c)$ At distance $3r$:$B_{3r} = B 	imes \frac{r}{3r} = 1 	imes \frac{1}{3} = \frac{1}{3} \ T$.Thus,the values are $2 \ T, \frac{1}{2} \ T, 	ext{ and } \frac{1}{3} \ T$.

$A$ long current-carrying wire produces a magnetic field of $1 \ T$ at a distance of $r$. What will be the magnetic field at distances of $(a)$ $\frac{r}{2}$,$(b)$ $2r$,and $(c)$ $3r$?

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