The field strength of a magnet (H) at a point on an axis, distance x from its centre, is given by the following equation:
H = M/2l [ [(1/(x-l)^2] - [1/(x+l)^2] ], where 2l = length of magnet and M = moment. Show that, if l is very small compared with x, then H = 2M/x^3.
Well I don't think it's as hard as you think actually.
Ok so here is what you have now:
Work out the top:
Now reduce what you can on top:
You were told that l is considerably smaller than x, so you can do this:
Please don't just copy that understand. You should understand why I did each step. Most of these kinds of problems can be solved quite easily by simplifying them first.
TrevorP beat me to it. My solution is longer/messier
because I wanted to include the final steps.
If is very small compared with , then the fraction is very small.The field strength of a magnet (H) at a point on an axis,
distance x from its centre, is given by the following equation:
. . .where = length of magnet and = moment.
Show that, if is very small compared with , then: .
Simplify the equation: .
. . and we have: .
In denominator, multiply by twice: .
Now consider what happens when is very small . . .
. . . . . . ta-DAA!
I need a nap . . .