A flexible circular loop 6.50 cm in diameter lies in a magnetic field with magnitude 1.35 T, d

A flexible circular loop 6.50 cm in diameter lies in a...

A flexible circular loop $6.50 \mathrm{~cm}$ in diameter lies in a magnetic field with magnitude $1.35 \mathrm{~T}$, directed into the plane of the page as shown in Fig. P29.51. The loop is pulled at the points indicated by the arrows, forming a loop of zero area in $0.250 \mathrm{~s}$. (a) Find the average induced emf in the circuit. (b) What is the direction of the

Key Concepts

Magnetic Flux

Magnetic flux is a measure of the quantity of magnetic field passing through a given area. It is calculated as the product of the magnetic field strength and the area of the loop perpendicular to the field. In problems involving changing areas or magnetic fields, the variation in the magnetic flux is what drives the induction of an emf.

Faraday's Law of Induction

Faraday's Law of Induction states that a changing magnetic flux through a loop or coil induces an electromotive force (emf) in the circuit proportional to the rate of change of the flux. This concept is central to analyzing how changes in loop geometry or magnetic field cause induced currents and voltage in the loop.

Lenz's Law

Lenz's Law provides the direction of the induced current resulting from a changing magnetic flux. It states that the induced current will flow in a direction such that the magnetic field it creates opposes the change in the original magnetic flux. This principle is essential for determining the polarity and direction of induced currents in electromagnetic systems.

Transcript

00:01 Hi, the problem here this is the uniform magnetic field directed into the plane of page perpendicularly in which there is a circular loop connected with a circuit like this this is resistance r these are the points a and b then this loop is pulled outward at these two points and its area, its final area is reduced to 0 when initial area was pi into r square.

01:02 And this is reduced to 0 in a time t given as 0 .250 second.

01:14 Of the loop was 6 .50 centimeters so its radius is half of the diameter means 0 .650 divided by 2 centimeter or we can see this is here this is 6 .50 so the radius will come out to be 3 .25 centimeter or 3 .25 into 10 x .5 meter magnetic field directed into the plane of paper is given as 1 .35 tesla.

01:56 So in the first part of the problem, the emf induced in this much duration of time will be given by faraday's laws of electromagnetic induction which says emf induced is equal to minus d5 by d t or we can say this is a negative of 5 -2 minus 5 -1 divided by time or we can say for 5 -2 this is b into a 2 for 5 -1 this is b into a 1 divided by time then we can take this area and this magnetic field as a common out so amf induced is equal to minus b a 2 minus a 1 by t so finally it becomes my minus b, 0 minus pi r square by t.

02:53 Or we can say this is b.

02:55 This is pi into b r squared divided by time.

03:02 So plugging in all known values here, for pi this is 3 .14.

03:07 For magnetic field this is 1 .35 tesla.

03:14 Then the square of radius means 3 .25 into 10 dash per minus 2.

03:20 The whole square and divided by time which was 0 .250 second.

03:28 So it comes out to be 1 .79 into 10 dashpar minus 2 volt or we can say 17 .9 into 10 dashpar minus 3 volt or finally this is 17 .9 millivolt and here it becomes the answer for the first part of the problem...

Please give Ace some feedback