The square loop in Figure P 31.24 is made of wires with...

Key Concepts

Magnetic Flux

Magnetic flux is a measure of the total magnetic field passing through a given area. It is calculated by the product of the magnetic field strength, the area through which the field lines pass, and the cosine of the angle between the field lines and the normal to the surface. In induction problems, changes in either the field strength or the area (or the orientation) result in a change of flux that can induce an emf.

Lenz's Law

Lenz's Law provides the direction of the induced current generated by a changing magnetic flux. It states that the induced current will flow in such a direction that its own magnetic field opposes the change in the original magnetic flux. This principle ensures the conservation of energy and is key to understanding the behavior of electromagnetic induction.

Faraday's Law of Induction

Faraday's Law states that a changing magnetic flux through a closed circuit induces an electromotive force (emf) in the circuit. The magnitude of the induced emf is proportional to the rate of change of the magnetic flux through the loop, and the negative sign in the law reflects the fact that the induced emf opposes the flux change, according to Lenz's Law.

Ohm's Law

Ohm's Law relates the current flowing through a conductor to the voltage across it and its resistance. In circuits where an emf is induced, the current can be calculated by dividing the induced emf by the total resistance in the circuit. This fundamental relationship is essential for analyzing induced currents in electrical circuits.

Transcript

00:02 Hi, in the given problem there is a square loop as shown in the figure whose ends are a and b which is kept in a uniform magnetic field directed perpendicular to the plane of paper into it as shown here.

00:43 Each side of this loop is having a value of 3 .00 centimeter and this inward magnetic field is having a value of 0 .100 tesla.

01:03 Now these opposite ends of this square loop are pulled apart by applying a force such that after some time.

01:18 The gap between the distance between the ends a and b is reduced to just 3 centimeter.

01:34 This end a will become a dash, this end b will become b dash and the distance between a dash and b dash is now just 3 centimeter.

01:47 While initially being a diagonal of the square it was having an expression side root 2 it was having a value of 3 .00 into square root of 2 centimeter but now it is reduced to 2 to 3 centimeter so initially area of the loop was a 1 is equal to square of side means to say we can say this is the square of 3 centimeter square which becomes nine centimeter square or we can say this is nine into ten dash bar minus four meter square now when the distance between a dash and b dash has been reduced to three centimeter actually these are two equilateral triangles joint with each other across the base because each side is having a value of 3 cm and the distance is also distance between a dash and b dash is also 3 cm so that we can say these are the two equilateral triangles joined side by side hence final area of the loop can be given as twice of area of an equilateral triangle equilateral triangle.

03:40 So we know the expression for equilateral triangle for the area of equilateral triangle is square root of 3 divided by 4 multiplied by the square of of si.

03:56 So putting these values here, a2 comes out to be 2 root 3 by 4 into square of 3.

04:09 So so here it comes out to be 7 .79 centimeter square or we can say this is 7 .79 into 10 ratio minus 4 meters square.

04:23 So this area of the loop has been reduced.

04:27 So the magnetic flux passing through it will also reduce and it has taken place in a short duration of time dd is equal to 0 .1 .00 second.

04:38 So, due to this change in magnetic flux linked through the loop an emf and hence an electric current will flow and emf will be induced so an electric current will also pass through this loop.

04:52 Hence, using faraday's laws of electromagnetic induction, emf induced will be given by using faradies laws of electromagnetic induction.

05:06 This is negative of time rate of change of magnetic flux.

05:10 Linked through this loop.

05:11 So this is minus d by dt into b a.

05:17 So here this is, so it can be written as b being a constant as the magnetic field is not changing can be taken out.

05:29 So this is d a by dt or we can write it like minus b into the change in area a2 minus a1 divided by d t so finally plugging in all the known values for magnetic field this is 0 .100 tesla for the change in area this is a 2 which was 7 .79 minus a1 was 9 into 10 dash per minus 4 meter square can be taken as a common out and for d t this was 0 .10 so, finally, this value of emf induced comes out to be 1 .21 into 10 dashpar minus 4 volt...

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