A magnetic field passing through two coils of the same...

A magnetic field passing through two coils of the same diameter and length decreases from a magnitude of $B_{\text {ex }}$ to zero in the time interval $\Delta t .$ The first coil has twice the number of turns as the second. (a) Compare the emfs induced in the coils. (b) How can you change the experiment so that the emfs produced in them are the same?

Key Concepts

Faraday's Law of Electromagnetic Induction

This fundamental law states that a change in magnetic flux through a circuit induces an electromotive force (emf) in the circuit proportional to the rate of change of the flux. The induced emf is given by the negative time derivative of the magnetic flux, illustrating how variations in the magnetic environment of a coil lead to electrical currents.

Magnetic Flux

Magnetic flux measures the total magnetic field passing through a given area and depends on both the strength of the magnetic field and the area it penetrates. In coil experiments, the flux is calculated by considering the magnetic field's orientation and the area of the coil, and a change in this flux over time is what induces an emf.

Effect of the Number of Turns on Induced Emf

The number of turns in a coil directly affects the induced emf because each loop experiences the change in magnetic flux. According to Faraday's Law, the total induced emf in a coil is the sum of the emfs induced in each individual turn. Therefore, a coil with more turns will experience a proportionally higher induced emf for the same rate of change in flux.

Transcript

00:01 Hi, in the given problem we are dealing the cases of two different coils.

00:08 The initial magnetic field passing through the coil is same for both of the coils.

00:16 Means b1 is given as b external for both of the coils.

00:23 B1 is this and this magnetic field is reduced to 0 in the both coils.

00:30 B2 is equal to zero the time taken for this magnetic field to reduce to zero is delta t again same for both the coils but the number of turns in the first coil is twice to that in the second coil hence we can say if number of turns here means n1 is n or we can say this is simply n not n1 n is an initial number of terms not initial just number of turns in the first void then n dash here will become n by two so in the first part of the problem we have to obtain the ratio of the emf induced in these two coils we have to compare the emfs induced in the coil so using the expression for emf induced as per faraday's laws of electromagnetic induction it says emf induced is given as negative of n times of t by t t what we can say this is negative of n times of d into b a by d t so here this e by e dash means the ratio of emf in the first coil to that in the second coil will come out to be minus n into the change in magnetic flux will be simply bx as dv is final magnetic field minus initial magnetic field so this is b2 for b2 this is zero for b1 this is b x so dv is negative of b x and for area you can use this a here and for time, this is also same delta t.

02:59 So we can say this is n into bx a by delta t.

03:05 For the first oil, divided by the emf inducing the second oil, that will be minus n by 2.

03:13 And same, the change in magnetic field, negative of bx into area that is also same.

03:20 Time taken delta t that is also same hence here it will come out to be n d x a by 2 delta t so if we cancel all these known values this ratio of emph induced comes out to be 2 is to 1 which is the answer for the first part of the problem now in the second part of the problem we have to find method by which without making any change in the constructions of the coil, we may have the same emf induced...

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