A ring of charge is centered at the origin in the vertical direction. The ring h

Question

A ring of charge is centered at the origin in the vertical direction. The ring has a charge density of lambda = 7.42 Times 10^-6 C/m and a radius of R = 2.57 cm. Find the total electric field, E, of the ring at the point P = (2.25 m, 0.00 m). The Coulomb force constant is k = 1/(4 pi epsilon_0) = 8.99 Times 10^9 N.m^2/C^2. Find the expression for the electric field, E, of the ring as the point P becomes very far from the ring (x >> R) in terms of the radius R, the distance x, the total charge on the ring q, and the constant k = 1/(4 pi epsilon_0).

Explanation / Answer

q = charge on the ring = change per unit length x circumference = 7.42 x 10-6 x 2 x 3.14 x 0.0257 = 1.2 x 10-6 C

Electric field by a ring at any point at distance "x" from the center along the axis is given as

E = k qx / (R2 + x2)(3/2) = (9 x 109) (1.2 x 10-6 ) (2.25) / (0.02572 + 2.252)3/2 = 2132.92 N/C

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