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SA magnetic field passing through two identical coils...

Key Concepts

Role of Coil Turns in Induction

The induced emf in a coil is directly proportional not only to the rate of change of magnetic flux but also to the number of turns in the coil. Each loop of the coil experiences the changing flux, and with more turns, the total induced emf is the sum of the individual contributions from each turn. Thus, a coil with twice the number of turns will have twice the induced emf under the same conditions.

Experimental Adjustment for Uniform Induced EMF

To achieve the same induced emf in coils with different numbers of turns, one can modify the experimental parameters so that the product of the number of turns and the rate of change of magnetic flux is equal for both coils. This can be accomplished by adjusting factors such as the rate of change of the magnetic field or the effective area of the coils, ensuring that the overall effect of the number of turns is counterbalanced.

Faraday’s Law of Induction

This principle states that an electromotive force (emf) is induced in a circuit whenever there is a change in the magnetic flux through it. The magnitude of the induced emf is proportional to the rate at which the magnetic flux changes over time. This forms the fundamental basis for understanding how changing magnetic fields can generate electric currents in coils.

Magnetic Flux

Magnetic flux represents the total magnetic field passing through a given area, typically defined as the product of the magnetic field strength and the area perpendicular to it. The concept is crucial because the induced emf in a coil depends directly on the rate of change of magnetic flux through the coil.

Transcript

00:05 Emf induced in a coil is given by e equals negative d, f, d, t equals negative, d, d, d, t of number of tons, magnetic field, area of the coil, and cosine theta is the angle between b and a.

00:39 So with respect to time the coil number does not change the area does not change the orientation of the coil with respect to the magnetic field does not change so this comes out to be an a cosine theta times negative d b d t so if we have to compare the emf induced on coil one versus coil two it will be e1 over e2 is equal to number of turns in coil one by number of turns in coil two area of both of them are same and initially they are oriented identically so cosine theta for the first coil is equal to cosine theta for the second and then multiplied by negative dbt for the first coil and negative d b d t for the second coil which will come out to be n1 over n2 because everything else is identical now it is given that it is given that the first coil has got twice the number of tons so this is this value is two so answer of part a is emf induced in coil 1 equals twice the emf induced in coil 2 now let us solve the second part now part b they are saying how can you have e1 equals e2 one thing that i should mention over here which is not important to this problem is change in magnetic field divided by change in time equals change in time is given us delta t so we don't have to worry about that whenever there is a change involved it is always final minus initial final value of magnetic field is zero initial value is b x which comes out to be negative b ex over delta we will not need this we will not need this in this problem but i just want to give this part to you all okay now how can we have u1 equals e2 we do not we will not be able to change anything else other than the cosine theta over here so i am going to write what will happen when e1 equals e2 e2 we know that we know that for in order to have e1 equals e2 we have to have n1 times a times cosine theta 1 times the negative of dbddd which will come out to be i don't want to write dbdt anymore however i can but i am just going to write b x over delta t equals n2 a cosine theta 2 b x over delta t if we cancel all of the common terms then we are left out with n1 cosine theta 1 equals remember over here we use n2 equals n2 equals 2 equals 2 n2 equals half n1 so we are going to use n2 equals half n1 times cosine theta 2 or we find cosine theta 2 equals 2 cosine theta 1 so this is how we can change the orientation of the coil such that the coil that has got more number of turn has got half the footprint...

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