Question

   A flat coil of wire is placed in a uniform magnetic field that is in the y direction. (i) The magnetic flux through the coil is maximum if the coil is (a) in the xy plane(b) in either the xy or the yz plane (c) in the xz plane (d) in any orientation, because it is constant. (ii) For what orientation is the flux zero? Choose from the same possibilities.

Answer 1

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)