Question

Plane of both loops circle and ellipse are held perpendicularly to the uniform magnetic field of strength B, Compare the magnetic flux passing through both loops if ${\varphi }_c$, the magnetic flux through the circular loop and ${\varphi }_E$, the magnetic flux through the elliptical loop given that area of both loops are same.

• A. ${\varphi }_c=2.5{\varphi }_E$
• B. ${\varphi }_c=\sqrt{2.5}$
• C. ${\varphi }_c={\varphi }_E$
• D. ${\varphi }_E=\sqrt{2.5}{\varphi }_c$
• E. ${\varphi }_E=2.5{\varphi }_c$

Answer 1

Answer: (C)

${\varphi }_c={\varphi }_E$

Magnetic flux linked with the circle

${\varphi }_C=\overrightarrow{B}.\overrightarrow{\Delta A}=BA\cos 0=BA$

Magnetic flux linked with the ellipse

${\varphi }_E=\overrightarrow{B}.\overrightarrow{\Delta A}=BA\cos 0=BA$

where $\overrightarrow{\Delta A}$ is the area vector which is parallel to magnetic field as given that field is perpendicular to the planes of both loops that's why $\theta$ is taken 0,

from above two equation it is clear that ${\varphi }_C={\varphi }_E$

as given magnetic field is same for both loops and area of both loops is equal.