The electric potential V at a distance R along the axis perpendicular to the center of a charged disc with radius a and constant charge density d is give by(adsbygoogle = window.adsbygoogle || []).push({});

V = 2pi*d*(SQRT(R^2 +a^2) - R)

Show that for large R

V = pi*a^2*d / R

This is what I have done so far...

V = 2pi*d * (SQRT(R^2 * (1+ a^2/R^2)) - R)

V = 2pi*d*R (SQRT(1 + a^2/R^2) - R)

V = 2pi*d*R * ( 1 + (1/2)(a^2/R^2) + (1/2)(1/2 -1)/2! * (a^2/R^2)^2 + ... - R)

V = 2pi*d*R * (1/2) (1/2 + a^2/r^2 - (1/2)/2! * (a^2/R^2)^2 + ... - R)

V = pi*d* R ( 1/2 + a^2/R^2 - (1/4)*a^4/R^4 + ...-R)

V = pi * d * R/R^2 (1/2 + a^2 - (1/4)a^4/R^2 + ...-R)

V = pi * d *R (1/2 + a^2 - (1/4)a^4/R^2 + ...-R)

V = pi *d * a^2/R (1/2a^2 + 1 - (1/4) + ...-R)

Am I doing this correctly. How do I simplify what is in the parenthesis to get 1, which multiply to give me pi*d*a^2/R?

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# Application of Taylor Series

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