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 = 6. 93 times 10-6 C/m and a radius of R = 3. 41 cm. Find the total electric field, E, of the ring at the point P = (1. 10 m, 0. 00 m). The Coulomb torce constart Is k= 1/(4pi 0) = 8. 99 times 109 N m2/C2. 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/(4pi 0).

Explanation / Answer

a)E=2rkx/(x2+r2)1.5

Substituting values

E=11028N/C

b)The equation for x>>R reduces to

E=2rk/x2

or the ring behaves like a point charge.

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