00:01
Hi, here in this given problem first of all this is the straight current carrying conductor having infinite length carrying current towards left and this is the rod moving parallel to the rod parallel to this current carrying conductor but in a direction opposite to the direction of current means it is moving towards right.
00:30
Lower end of this rod is at a distance a from the wire and its upper end that is at a distance b from the conductor.
00:47
Here this value of a that is given as 1 .0 mm value of b that is 20 mm.
00:56
Speed of the conductor v that is 5 .0 m per second.
01:06
We differentiate this conductor into small element and take such an element having a width dx at a distance x from the conductor.
01:21
We differentiate the rod into small elements each having a width dx and take one such element at a distance x from the straight wire.
02:16
Current in this wire that is given to be 80 ampere.
02:37
So small motional emf induced across that small element that will be given by dv is equal to magnetic field at this position due to the current carrying conductor multiplied by its speed multiplied by its length.
03:10
And this magnetic field is given as mu0 upon 4 pi using bryant severs law that is mu0 upon 4 pi into 2i by distance which is x.
03:21
So this dv will be given by mu0 by 4 pi multiplied by 2i by x into v into dx.
03:32
So total emf induced across the conductor across the rod that will be given by integrating both the sides.
03:52
And in the integration of right hand side constants will come out which includes mu0 upon 4 pi 2i v integration of 1 by x dx limits of x from a to b...