A flat coil is in a uniform magnetic field. What angle between the magnetic field and the plane of the coil produces the maximum flux, and what angle produces 90% of the maximum flux

This question is incomplete, the complete question is;

A flat coil is in a uniform magnetic field. What angle between the magnetic field and the plane of the coil produces the maximum flux, and what angle produces 90% of the maximum flux

A) max: 0°

90% of max: 90°

B) max: 90°

90% of max: 45°

C) max: 90°

90% of max: 64°

D) max: 0°

90% of max: 26°

E) max: 90°

90% of max: 80°

Option C) max: 90°

90% of max: 64°  is the correct Answer

Explanation:

from the Suppose Area is A.

then flux at angular position O is

Ф = BAsin∅

⇒ Ф = βmaxSin∅

flux will be max when sin∅ = 1

therefore sin∅ = 1

∅ = sin⁻¹ 1

∅ = 90°

Now at 90% of max flux

Ф ⇒ 0.9βmax = βmax sin∅

0.9 = sin∅

∅ = sin⁻¹ (0.9)

∅ = 64.15° ≈ 64°

Therefore Max ∅ = 90°

90% flux = 64°

Option C) max: 90°

90% of max: 64°  is the correct Answer