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Net magnetic field at the centre of the circle $O$ due to a current carrying loop as shown in the figure for $ \theta < 180^{\circ}$ is

$\begin {array} {1 1} (a)\;Zero \\ (b)\;Perpendicular\: to\: the\: paper\: inwards \\ (c)\;Perpendicular \: to \: the\: paper\: outwards \\ (d)\;Is \: perpendicular\: inwards\: or\: outwards\: depending\: on\: the\: value \: of \: theta \end {array}$

 

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A)
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Calculate the fields due to the two segments and add them up. the direction of field due to the circular part of the loop isperpendicular to the paper inwards and due to the straight portion of loop is outwards.
They will be in opposite directions and the field due to the straight wire dominates as it is nearer the centre O.
Ans : (c)

 

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