Finding the B-field at a point outside ring of current IN Plane of ring

[maxmax1]

Homework Statement

Determine the B field at a point P with distance d from centre of current ring radius r (d>r ie outside ring of current) but IN the Plane of ring (i.e off the axis)

Homework Equations

Biot savart: db=(u.I/4pi.r^2).dl.sinx

u=mu, I=current, x=angle made with current vector element dl and vector r connecting P to dl.

The Attempt at a Solution

the angle x will vary at all points along ring with vector joining point P, as will r.

I will integrate from 0 to 2pi my expression for db but with r^2=a^2+d^2-2adcosy

where y is angle between radial vector and d.

I am stuck because cannot determine how to express y in terms of x. and thus cannot integrate!

many thanks!

 

[tiny-tim]

I am stuck because cannot determine how to express y in terms of x. and thus cannot integrate!

Hi maxmax1!

Hint: P is at (d,0).

The tangent at Q = (r cosy, r siny) is … ?

So the angle betweent he tangent and PQ is … ?