1 a 12 turn coil 10 cm in diameter has its axis parallel to...

A 12-turn coil, 10 cm in diameter, has its axis parallel to a magnetic field of 0.5 T, which is produced by a nearby electromagnet. The current in the electromagnet is cut off, and an average emf of 8 V is induced in the coil. (a) What is the change in the flux through the coil? (b) How much time is required for the field to disappear? 2. The cables that connect the starting motor of a car with its battery are 1.0 cm apart for a distance of 40.0 cm. (a) Find the magnitude of the force between the cables when the current in them is 300.0 A. (b) What should be the distance between the cables for the force between them to be 2.0 N?

Transcript

00:02 Hi, here in this given problem and there are two problems, there are two different questions in this problem in question above one.

00:10 Number of turns in the coil, these are 12.

00:14 Diameter of the coil is 12 centimeters, so its radius r will be half of the diameter.

00:24 Means this is 6 cm or we can say this is 6 into 10 dash per minus 2 means.

00:33 Initially magnetic field linked through the coil.

00:38 Magnet field is due to electromagnet and that is 0 .5 tesla.

00:44 The magnetic field vector is having an angle of 0 degree with the area vector.

00:50 And finally when the current in the electromagnetic is in electromagnetic is switched off, this magnetic field will also drop to 0 and it is given that emf induced as a result of change in the magnetic field and hence the change in the magnetic flux that is given as 8 volt the average emf induced so in the first part of the problem we have to find the change in magnetic flux and that change in magnetic flux delta phi will be given by final flux minus initial flux now as finally there is no magnetic field first of all we will use an expression for the magnetic flux and that is b .a so this is b1 .a and that is b2 dot a minus b1 .a.

01:56 So here it will be 0 for the final magnetic flux as b2 is 0 and for initial one this is b1a cost theta and theta is 0 degree and cos 0 degree comes out to be equal to 1 only.

02:08 So here it is for b1 that is 0 .5 minus 0 .5 tesla multiplied by the area pi r square for pi this is 3 .14.

02:19 For radius this is 6 into 10 to the power minus 2 square.

02:25 So finally this change and yeah of course the total change in flux for total change in flux it should be multiplied by the number of turns in the coil also and that is to well so finally this flux magnitude of the flux if we look for ignoring the negative sign this magnitude of the magnetic flux will come out to be equal to 6 .78 into 10 to the power minus 2 weber and this is the answer for the first part of this question number one here then in the second part part we have to find time taken for this magnetic field to drop to zero.

03:21 So using faraday's laws of electromagnetic induction, emf induced is given by minus d -5 delta -fi delta -t, the time date of change of magnetic flux.

03:34 So this is minus.

03:35 Now taking this change in flux with a negative sign, this is minus 6 .78 into 10 to the power minus 2, weber divided by time which is not known to us.

03:48 We have to find it...

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