00:01
Hi, in the given problem, radius of the wire loop is given as r is equal to 2 .00 cm, or we can say this is 2 .00 into 10 dash per minus 2 meter.
00:26
Resistance of the wire used in making this loop is r is equal to 0 .600 o.
00:37
Initial magnetic field is 3 .00 tesla after which the magnetic field varies with the time as a function of time as b is equal to v0, e -res to the power minus t by tau, where the value of this tau is 0 .5502.
01:02
In the first part of the problem we have to find the expression, first of all, for the magnetic flux linked with the coil, then with the help of that magnetic flux, the emf induced in the coil, and after which we have to find current passing through this coil.
01:25
So first of all, the magnetic flux linked with the coil will be given as phi is equal to b .a, which we can.
01:39
Comes b a cos theta now as initially the plane of oil is perpendicular to the magnetic field so angle between area vector and magnetic field is 0 degree so we can say this is b a cause 0 degree and cos 0 degree is 1 so it comes out to be b into a only and we know the value of the function of b is given as b0 into e minus t by 0 .5 for the value of tau.
02:20
Then for area, this is pi into r square.
02:26
So finally, this flux here comes out to be for pi r squared.
02:35
This is 2 into 10 dash bar minus to the whole square for b not this is 3 tesla then e ratio power minus t by 0 .5 if we calculate it putting the value of this pi also here we get 5 is equal to 3 .768 into 10 dashed bar minus 3, e -res the power minus t by 0 .5 weber.
03:28
As this is the magnetic flux, so we'll be having a unit of weber.
03:38
Now, with the help of faradies laws of electromagnetic induction, the expression for emf is given as negative of time derivative of the function of magnetic flux, means minus d5 by dt.
04:10
So it becomes, if we differentiate it, here this is a constant, we remain as it is, minus 3 .768 into 10 dash to per minus 3.
04:23
Then differentiation of e to the power x is same as e to the power x means e to the power minus t by 0 .5.
04:31
Then differentiation of this power of e, which comes out to be just, minus 1 .0 .5.
04:42
So finally it becomes emf induced is equal to 7 .536 into 10 dashed par minus 3.
04:54
E...