I have a rectangular sheet of given dimensions say L wide and H high. Out of each point some variable field is flowing through given by rules as follows:(adsbygoogle = window.adsbygoogle || []).push({});

Consider the top left corner of the sheet, the field is perpendicular at that point. As one moves from top left corner to the top right corner the field remains same in magnitude but changes in direction such that at the top right corner it is horizontal to the surface. The change in the direction is uniform.

This happens in whole of the sheet, that the field is perpendicular to the sheet at the left most side and gradually becomes horizontal at the right most ride.

We need to find the flux coming out of the sheet. (NOTE: This is not a homework problem, or I would have posted it in the homework section)

My Steps:

1) I first of all considered the equation of such a field. Since I am interested only in the perpendicular component of field, I made the equation of perpendicular component only.

Such a field V maybe given by V(y) = Asin(pi/2 - (x*pi/2L))

where V(y) is the perpendicular component of the field and A is the max of field. See that at x = 0, field is wholly perpendicular and at x=L field is wholly horizontal.

2) Next I considered a small area element on the sheet of H*dx because a vertical strip (may) simplify my calculations (as the field is constant each vertical strip)

3) The flux through such an element is given by

H * Asin(pi/2 - (x*pi/2L)) dx

4) We obtain the net flux by integrating over the region r as

int(H * Asin(pi/2 - (x*pi/2L)) dx) from 0 to L

which gives -2LAH/pi

Since I don't have any answer to the problem please tell me if my solution is correct, otherwise point the mistakes in it. Any other suggestions are welcomed.

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# I have a rectangular sheet of given dimensions say L wide and H high.

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