Question

In a physics laboratory experiment, a coil with 200 turns enclosing an area of 12 cm2 is rotated in 0.040 s from a position where its plane is perpendicular to the earth’s magnetic field to a position where its plane is parallel to the field. The earth’s magnetic field at the lab location is 6.0×10−5 T. (a) What is the magnetic flux through each turn of the coil before it is rotated? After it is rotated? (b) What is the average emf induced in the coil?

Answer 1

To solve this problem it is necessary to apply the concepts related to the magnetic flow of a coil and take into account the angles for each case.

It is also necessary to delve into part C, the concept of electromotive force (emf) which is defined as the variation of the magnetic flux as a function of time.

By definition the magnetic flux is determined as:

$\phi = NBA cos\theta$

Where

N = Number of loops $\rightarrow$ We will calculate the value for each of the spins

B = Magnetic Field

A = Cross-sectional Area

$\theta =$ Angle between the perpendicular cross-sectional area and the magnetic field.

PART A) The magnetic flux through the coil after it is rotated is as follows:

$\phi_i = NBA cos\theta$

$\phi_i = (1turns)(6*10^{-5}T)(12*10^{-4}m^2)cos(0)$

$\phi_i = 7.2*10^{-8}T\cdot m^2$

PART B) For the second case the angle formed is perpendicular therefore:

$\phi_f = NBA cos\theta$

$\phi_f = (1turns)(6*10^{-5}T)(12*10^{-4}m^2)cos(90)$

$\phi_f = 0$

PART C) The average induced emf of the coil is as follows:

$\epsilon = - (\frac{\phi_f-\phi_i}{dt})$

$\epsilon = -(\frac{0-7.2*10^{-8}}{0.04})$

$\epsilon = 1.8*10^{-6}V$