In: Physics
Expression for Magnetic flux is,
$$ \begin{aligned} (\varphi) &=\vec{B} \cdot \vec{A} \\ &=B A \cos (\theta) \end{aligned} $$
Here, \(\theta\) is the angle between magnetic-field and Areal vector.
\((a)\)
In the \(x z\) plane, the magnetic Field producedaround the coil and parallel to each other. Then the flux is maximum. Then angle between \(\vec{B}\) and \(\vec{A}\) is \(0^{\circ}\)
$$ \begin{aligned} (\varphi)_{\max } &=B A \cos 0^{\circ} \\ &=B A \end{aligned} $$
Therefore the corret option is \((c)\)
(b) In the xyor \(\mathrm{y} z\) plane, the magnetic Fieldproduced around the coil and normal to each other.Then the flux is, Then angle between \(\overrightarrow{\mathrm{B}}\) and \(\overrightarrow{\mathrm{A}}\) is \(90^{\circ}\)
$$ \begin{aligned} (\varphi)_{\operatorname{mxx}} &=B A \cos \left(90^{\circ}\right) \\ &=0 \end{aligned} $$
Therefore the corret option is (b)