Question 11: Follow link below http://imgur.com/UUrZxwk A ring of charge is cent

Question

Question 11: Follow link below

http://imgur.com/UUrZxwk

A ring of charge is centered at the origin in the vertical direction. The ring has a charge density of lambda = 4.48 times 10^-6 C/m and a radius of R = 1.87 cm. Find the total electric field, E, of the ring at the point P = (1.79 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_infinity, 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

  If the ring has 4.48 x 10^-6 Coulombs per meter, then the total charge is just that number times the circumference of the ring, 2*pi*R.=2*pi*1.87

=11.74 n/c
In fact that's why there's a 2*pi*R* in the numerator of the first formula.

2*pi*R*=2pi *1.87*4.48*10^-6

=5.26*10^-5

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