00:01
Here, given that, e vector is equal to 2y square plus z, i plus 4 xyj plus xk over epsilon node volt per meter.
00:09
Here, first we find the volume charge density.
00:13
And we know divergence of e vector is equal to volume charge density over epsilon node.
00:24
From this, we obtain rov is equal to epsilon node divergence of e vector.
00:33
Now this becomes equal to absalom 0 dl over dlx i plus z dl over dly plus k dl over del z d d d d vector here e vector is equal to 2y square plus zi plus 4x y j plus epsilon node here a epsilon node is the constant so it comes outside this differentiation we obtain rovi is equal to a epsilon note or epsilon not and the dot product becomes equal to del over del x 2 y squared plus j plus del d d 'uil 4xy plus del over d d d d x and by simplifying this we obtain rovi is equal to this becomes equal to 0 and this becomes equals to 4 x and this also becomes equal to 0 here we are asked to calculate the value of row v 8 negative 1 comma 0.
02:02
3 so from this we we obtain the value of row 8 negative 1 comma 0 .3 is equal to 4 into negative 1 so from this we obtain the value of prov is equal to negative 4.
02:16
And the unit of volume chart density is equal to column per meter cube.
02:23
Now next we solve part b.
02:25
In part b we are asked to calculate the flux passing through the cube which is defined by x from 0 to 1, y from 0 to 1 and z from 0 to 1.
02:35
And we know flux passing through a closed surface is given by 5 is equal to close integration, close double integration of e vector, ds vector.
02:52
And by using ghost law, this is equal to q over epsilon node...