00:01
Hello students here we have the magnetic field b vector equal to 3x a x vector plus minus 3 x square y plus 9 x square a y vector plus 2 y minus 3 z plus 3 x square z a z vector.
00:13
So here we have to calculate the magnetic flux.
00:15
So magnetic flux can be determined over a surface as phi equal to double integral over a surface into b d s vector.
00:23
So here we can write down the s vector as s x equal to x comma x square plus y square because we have the parabola surface here y equal to x square plus z square.
00:36
So substituting it at calculating the derivatives dou s by dou x and dou y by dou z that is 1 comma 2 x comma 0 and 0 comma 2 z comma 1.
00:47
So from this we can get the normal vector as dou s divided by dou x cross dou s divided by dou z.
00:53
So we will get the cross product as 2 x comma minus 1 minus 2 z.
00:59
Then we can get the normal vectors amplitude magnitude as square root of 4 x square plus 1 plus 4 z square.
01:05
So the unit normal is the vector divided by its magnitude and then we can get the d s vector as cross product between dou s by dou x and dou s divided by dou y into dx dz.
01:19
So we will get d s vector as 2 x a y minus i a y plus 2 z a z magnitude into dx dz...