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  4. An electric current passes through a long straight wire. At a distance 5 cm from the wire, the magnetic field is B. The field at 20 cm from the wire would be

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Q. An electric current passes through a long straight wire. At a distance $5\, cm$ from the wire, the magnetic field is $B$. The field at $20 \,cm$ from the wire would be

AFMCAFMC 2009

Solution:

For a long straight wire, the magnetic field
$B=\frac{\mu_{0} 2 I}{4 \pi r}$
image
When $ r=5\, cm$
$\therefore B=\frac{\mu_{0} 2 I}{4 \pi(5)}\,\,\,\,....(i)$
Similarly, when $r=20 \,cm$
$B'=\frac{\mu_{0} 2 I}{4 \pi(20)}\,\,\,\, ...(ii)$
From Eqs. (i) and (ii), we get
$B'=\frac{B}{4}$