Plese Help!! im not sure how to do this what so ever!!! The equation for the mag

Question

Plese Help!! im not sure how to do this what so ever!!!

The equation for the magnetic field B at a point P on the axis of a single flat coil of N turns with current i is gamma = B = mu 0I R2 N / 2(R2 + x2)3/2, where x is the distance along its axis from the center of the coil to the field point P. Derive the equation for the magnetic field at the midpoint between the centers of the Helmholtz coils. This is the expression given in . Helmholtz coils consist of twg coils separated by a distance equal to the coil radius. (You will have to use the above equation twice.) Simplify your answer to a numeric multiple offmu0iN/R. Clearly show your work.

Explanation / Answer

at a dstance x from the center of a coil, B = mue*I*R^2*N/(2* (R^2+x^2)^(3/2) )

here, we have two coils and the distance between the two coils is R.

and We need to find magnetic field due to the two coils at midpoint between them.

so,x = R/2

Bnet = B1 + B2

= mue*I*R^2*N/(2* (R^2 + (R/2)^2)^(3/2) ) + mue*I*R^2*N/(2* (R^2 + (R/2)^2)^(3/2) )

= 2*mue*I*R^2*N/(2* (R^2 + (R/2)^2)^(3/2) )

= mue*I*R^2/( (5/4)^(3/2) *R^3)

= 0.71554*mue*I*N/R <<<<<<-----------Answer

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