Question

8

8. (14 pts) A 16 nC charge is distributed uniformly along the x axis from x = 0 to x = 4 m. (a) Write down which of the following integrals is correct for the magnitude (in N/C) of the electric field at x = +10 m on the x axis: 10 154dx -, o (10-x)2 , Jo (10-x)2,Jo (b) Calculate the magnitude of the electric field at this particular position (x = +10 m on the x axis)

Answer 1

Dq = dx middot lambda lambda = 16nc/4m = 4 nc/m E = integral^10_6 kdq/X^2 = > E = integral^10_6 k middot lambda dx/X^2 = integral^10_6 9 times 10^9 times 4 times 10^-9/X^2 dx = integral^10_6 36 dx/x^2 = 36[-1/x]^10_6 = 36[-1/10 + 1/6] or it can also be written as E = integral^4_0 36dx/(10 - x)^2 E = integral^6_10 -36 dt/t^2 E = integral^10_6 36 dt/t^2 let (10 - x) = t -dx = dt x = 0: t = 10 u = 4 t = 6 square as about so answers will be square