Which of the following could double the emf produced when...

Which of the following could double the emf produced when the fly turns $90^{\circ} ?$ (a) Double the number of turns in the coil. (b) Double the coil's area. (c) Double the magnitude of the external magnetic field. (d) Get the tsetse fly to take twice as long to turn. (e) $a, b,$ and $c$

Which of the following could double the emf produced when the fly turns $90^{\circ} ?$
(a) Double the number of turns in the coil.
(b) Double the coil's area.
(c) Double the magnitude of the external magnetic field.
(d) Get the tsetse fly to take twice as long to turn.
(e) $a, b,$ and $c$

Key Concepts

Coil Parameters (Number of Turns and Area)

The coil’s physical properties, including the number of turns and the area of the coil, directly influence the magnetic flux linked with the coil. Doubling either the number of turns or the area leads to a proportional increase in the total magnetic flux, thereby increasing the induced emf if the rate of flux change remains constant.

Magnitude of the External Magnetic Field

The strength of the external magnetic field is directly related to the magnetic flux through the coil. An increase in the magnetic field’s magnitude increases the flux, which in turn can produce a higher induced emf according to Faraday's law, assuming the rate of change of the field remains the same.

Magnetic Flux

Magnetic flux is the product of the magnetic field strength, the area it penetrates, and the cosine of the angle between the field and the perpendicular (normal) to the area. It quantifies the amount of magnetic field passing through a coil, and any change in flux over time results in the induction of an emf.

Faraday's Law of Electromagnetic Induction

This fundamental principle states that an emf is induced in a circuit whenever there is a change in the magnetic flux through the circuit. The law shows that the magnitude of the induced emf is directly proportional to the rate at which the flux changes, which can be affected by factors such as the coil’s number of turns, area, and the strength of the magnetic field.

Transcript

00:02 Hi, these are the magnetic field lines in the given problem representing a uniform magnetic field.

00:14 In this magnetic field, the fly is flying over which there is a coil wound.

00:23 Initially the plane of coil was perpendicular to the direction of magnetic field and after some time the plane of this coil become parallel to the magnetic field.

00:38 So it has been asked in the given problem, which of the following could double the emf produced when the fly turns 90 degree here like this.

00:50 So in option a, double the number of turns in the coil.

00:56 So we know the emf induced is having an expression n times of d5 by d t or we can say this is n times of n times of d t.

01:04 Or we can say this is n times of b2 or we can say just 5 2 not b2 this is 5 2 the final flux minus initial flux so this is 5 2 minus 5 1 divided by time or we can say this is n times of b a cos 90 degree because finally the angle between area vector and magnetic field vector is 90 degree while initially it was 0 degree so this is b a cos 90 degree and this is minus so cost 90 degree and d a cause zero degree initially it was 0 degree divided by time so finally the expression for this emf induced comes out to be n b a by t this is minus here and this is 0 minus 1 so finally we can say emf induced is given by n b a by t so if we look at in option a, it says that double the number of turns in the coil.

02:17 So yes, this is sure.

02:19 The emf induced depends directly on the number of turns.

02:22 So on doubling the number of turns in the coil, the emf induced will become double.

02:27 So option a is correct.

02:29 In option b, double the coils area...

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