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Physics-

General

Easy

Question

In the figure shown, the magnetic field induction at the point $O$ will be

$\frac{μ_{0} i}{2 π r}$
$(\frac{μ_{0}}{4 π}) (\frac{i}{r}) (π + 2)$
$(\frac{μ_{0}}{4 π}) (\frac{i}{r}) (π + 1)$
$\frac{μ_{0}}{4 π} \frac{i}{r} (π - 2)$

The correct answer is: $open parentheses fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction close parentheses open parentheses fraction numerator i over denominator r end fraction close parentheses open parentheses pi plus 2 close parentheses$

Field due to a straight wire of infinite length is $fraction numerator mu subscript 0 end subscript i over denominator 4 pi r end fraction$ if the point is on a line perpendicular to its length while at the centre of a semicircular coil is $fraction numerator mu subscript 0 end subscript pi i over denominator 4 pi r end fraction$ .

$therefore B equals B subscript a end subscript plus B subscript b end subscript plus B subscript c end subscript$
$equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator i over denominator r end fraction plus blank fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator pi i over denominator r end fraction plus fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator i over denominator r end fraction$
$equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator i over denominator r end fraction open parentheses pi plus 2 close parentheses$ out of the page

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