In a physics laboratory experiment, a coil with 200 turns...

In a physics laboratory experiment, a coil with 200 turns enclosing an area of $12 \mathrm{~cm}^{2}$ is rotated in $0.040 \mathrm{~s}$ 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 $6.0 \times 10^{-5} \mathrm{~T}$. (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?

Key Concepts

Magnetic Flux

Magnetic flux represents the amount of magnetic field passing through a given area. It is calculated by multiplying the magnetic field strength by the area perpendicular to the field, and further modified by the cosine of the angle between the field direction and the normal (perpendicular) to the surface. This concept is fundamental in understanding how magnetic fields interact with surfaces and is essential for analyzing electromagnetic induction phenomena.

Faraday's Law of Electromagnetic Induction

Faraday's law states that a changing magnetic flux through a circuit induces an electromotive force (emf) in that circuit. The law quantitatively relates the induced emf to the time rate of change of the magnetic flux, and when applied to a coil, it also takes into account the number of turns, thereby revealing how variations in the orientation or strength of a magnetic field can generate electrical currents.

Effects of Coil Orientation

The orientation of a coil with respect to a magnetic field has a direct impact on the magnetic flux it encloses. Changing the angle between the plane of the coil and the magnetic field alters the effective component of the field passing through the coil, which in turn changes the magnetic flux. This concept is critical in applications where the rotation of a coil is used to produce a varying flux, leading to the generation of an induced emf as described by Faraday's law.

Transcript

00:01 Hi, in the given problem, the number of turns in the coil are n is equal to 200.

00:21 And area of the coil is a is equal to 12 centimeter square or we can say this is 12 into 10 dashed bar minus 4 meter square.

00:41 Initially, the plane of coil is perpendicular to the magnetic field means the angle between area vector and magnetic field is theta 1 is 0 degree and in a time duration of 0 .0 .0 second plane of the coil becomes parallel to the magnetic field means now the angle between area vector of the coil and the angle between area vector of the coil and.

01:11 Magnetic field becomes 90 degree.

01:17 Magnetic field in which this coil is rotating is given as b is equal to 6 .0 into 10 degrees of minus 5 tesla.

01:27 Now in the first part of the problem we have to find the magnetic flux through one turn.

01:36 So magnetic flux through each turn of the coil is given as 5 is equal to d .a.

01:57 Or we can say this is b a cost theta.

02:03 So initially before the coil starts rotating the flux will be given by 5 .1 is equal to 6 .0 into 10 dashpar minus 5 tesla into 12 into 10 dashed par minus 5 tesla into 12 into 10 dash par minus minus 4 meter square into cosine of 0 degree, which comes out to be 1, cause 0 degree is always 1.

02:32 So finally, this answer for the first answer for the first part of the problem, is flux linked through the one turn of the coil.

02:44 When it starts just to start rotating is 7 .2 into 10 dash minus 8 vapor.

02:53 First of the answer of this first part of the problem...

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