A coil has N turns enclosing an area of A. In a physics laboratory experiment, the coil is rotated during the time interval delta t from a position in which the plane of each turn is perpendicular to Earth's magnetic field to one in which the plane of each turn is parallel to the field. The magnitude of Earth's magnetic field at the lab location is B. What is the magnitude $final of the magnetic flux through the coil before it is rotated? What is the magnitude $final of the magnetic flux through the coil after it is rotated? What is the magnitude of the average emf induced in the coil? If a symbolic answer is required, your expression must include B, A, and any other variables.

A) magnitude of the magnetic flux through the coil before it is rotated = BA

B) magnitude of the magnetic flux through the coil before after it is rotated = 0

C) magnitude of the average emf induced in the coil = N|(BA)/Δt|

Explanation:

A) If we consider a loop of wire which has an Area (A) with number of turns as (N), it is initially placed perpendicular in the earth's magnetic field. It is now rotated from this position to a position where its plane is parallel to the field.

The earth's magnetic field at the position of the loop is denoted as B.

Thus, the flux through the loop before it is rotated is given by;

Φ_Bi = BACosθ

Before rotation, angle is 0

Thus,

Φ_Bi = BACos0 = BA

B) After it is rotated, the angle is now 90°.

Thus, Φ_Bf = BACos90 = 0

C) The average magnitude of the induced EMF in the coil equals the change in the flux divided by the time of change and multiplied by the number of turns.

Thus;

magnitude of the induced EMF =

|ε_av| = N |(Φ_Bf - Φ_Bi)/Δt|

From earlier, we saw that Φ_Bf = 0 and Φ_Bi = BACos0 = BA

Thus,

|ε_av| = N|(BA)/Δt|