A 664-turn circular-loop coil 18 cm in diameter is initially aligned so that its axis is parallel to Earth’s magnetic field. In 3.5 ms the coil is flipped so that its axis is perpendicular to Earth’s magnetic field. If an average voltage of 0.16 V is thereby induced in the coil, what is the value of Earth’s magnetic field at that location? Answer in units of µT.

Explanation:

Let the earth's magnetic field be H at that location .

Iniially the axis of coil is aligned with magnetic field so magnetic field must be perpendicular to face of the coil.

Initial magnetic flux passing through the coil

= n B A , n is number of coils , B is magnetic field and A is area of the face of the coil .

= 664 x B x π r²

= 664 x B x 3.14 x 9 x 9 x 10⁻⁴

= 16.89 B  Weber

When the coil is turned so that its face becomes parallel to the magnetic field , flux passing through it becomes zero.

change in flux = 16.89B - 0

= 16.89 B

time = 3.5 x 10⁻³ s

induced voltage = change in flux / time

= 16.89 B / 3.5 x 10⁻³

.16 = 16.89 B / 3.5 x 10⁻³

B = .16 x 3.5 x 10⁻³ / 16.89

= .033155 x 10⁻³

3.3155 x 10⁻⁵ t

33.155 x 10⁻⁶

= 33.155  µT.