In a physics laboratory experiment, a coil with 180 turns. Each turn of the coil encloses an area of 12 cm2 . The coil is rotated from a position where its plane is perpendicular to the earth's magnetic field to one where its plane is parallel to the field. The rotation takes 3.4×10−2 s . The earth's magnetic field at the location of the laboratory is 6.0×10−5 T.

A) What is the magnetic flux through one turn of the coil before it is rotated? The SI unit for magnetic flux is the Weber (Wb), which is equal to Tm^2.
B) What is the magnetic flux through one turn of the coil after it is rotated?
C) What is the average emf induced in the coil as it is rotated from the perpendicular to the parallel orientation?

A) Φ_i = 7.2 x 10^(-8) Wb

B) Φ_f = 0 Wb

C) EMF = 0.381 mV

Explanation:

We are given;

Area; A = 12 cm² = 12 x 10^(-4) m²

Magnetic Field; B = 6 x 10^(-5) T

Rotation time; t = 3.4×10^(-2) s = 0.034s

A) Magnetic flux is given by the equation;

Φ = BA•cosθ

Where;

B is the magnetic field

A is area

θ is angle to magnetic field

Now, at initial point where its plane is perpendicular to the earth's magnetic field, the angle is 0

Thus,

Φ_i = BA•cosθ = 6 x 10^(-5) x 12 x 10^(-4) x cos(0)

Φ_i = 7.2 x 10^(-8) Wb

B) Now, the coil is rotated to a place where its plane is parallel to the earth's magnetic field and thus, the angle here is 90°

Thus,

Φ_f = BA•cosθ = 6 x 10^(-5) x 12 x 10^(-4) x cos(90) = 0 Wb

C) The formula for average EMF induced is given by;

EMF = N[(Φ_f - Φ_i)/t]

Where N is number of turns, t is time while Φ_f and Φ_i have been calculated earlier.

Thus,

EMF = 180[(0 - 7.2 x 10^(-8))/0.034]

EMF = 180[(-7.2 x 10^(-8)/0.034]

EMF = - 3.81 x 10^(-4) V or - 0.381 mV

We want magnitude of the EMF, thus we will take absolute value of the EMF, so, we'll use;

EMF = 0.381 mV

Φθ