Question

If magnetic field \( B \) is perpendicular to surface area vector \( \mathbf{ds} \), then the magnetic flux on area \( ds \) will be:

• A. \( B\, ds \cos \theta \)
• B. \( B\, ds \sin \theta \)
• C. \( B\, ds \tan \theta \)
• D. zero

Hint:

Magnetic flux is maximum when \( B \) is parallel to \( \mathbf{ds} \) (\( \theta = 0^\circ \)) and zero when perpendicular (\( \theta = 90^\circ \)).

Answer 1

The Correct Option is D

Magnetic flux \( \Phi \) through area \( ds \) is given by: \[ \Phi = B\, ds \cos \theta, \] where \( \theta \) is the angle between \( B \) and the area vector \( \mathbf{ds} \). If \( B \) is perpendicular to \( \mathbf{ds} \), then \( \theta = 90^\circ \), so: \[ \Phi = B\, ds \cos 90^\circ = 0. \]