A rod of length 95 cm has a uniform linear charge density of 9 C/m. Determine th

Question

A rod of length 95 cm has a uniform linear charge density of 9 C/m. Determine the Electric Field at a point P located at a perpendicular distance 71 cm along a line of symmetry of the rod. Since the rod is not infinitely long, using Gauss's law does not make things simpler. Use superposition and integrate. (Your text, page 690, has a derivation of this setup.) Enviar RespetI Incorrecto. Tries 2/5 Anteriores Intentos Find the electric field at P if P were located at a distance 71 cm from one end of the rod, as shown.

Explanation / Answer

Given,

l = 95 cm ; lambda = 9 uC/m ; r = 71 cm

The E field will be given by:

E = lambda l/(2 pi e0 r) x 1/sqrt(l^2 + 4r^2)

E = 9 x 10^-6 x 0.095/(2 x 3.14 x 8.85 x 10^-12 x 0.071) x 1/sqrt (0.095^2 + 4 x 0.071^2)

E = 2.17 x 10^5 x 5.85 = 1.27 x 10^6 V/m

Hence, E = 1.27 x 10^6 V/m

In this case,

E = kq/[r (l + r)]

Q = lambda l = 9 x 10^-6 x 0.095 = 0.855 x 10^-6

E = 9 x 10^9 x 0.855 x 10^-6/[0.071 (0.071 + 0.095)] = 6.53 x 10^5 V/m

Hence, E = 6.53 x 10^5 V/m

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