Answer:
Maximum linear charge density = 84.14 nC/m
Explanation:
Looking at this question, The electric field of a line charge of infinite length is given
by : Er = (1/(2πεo)) x (λ/r)
r = the distance from the center of the line of charge
λ = the linear charge density of the wire.
Now looking at the equatiom, due to the fact that Er varies inveresely with r, its maximum value will occur at the
surface of the wire where r = R, the
radius of the wire:
And so, Emax = (1/(2πεo)) x (λ/R)
Let's make λ the subject of the equation and we get;
λ = 2πεo(REmax)
From the question, R = 0.55/2 = 0.275cm
Also, Emax = 5.50 × 10^(6)
N/C
Let's take the value of the electric constant to be εo = 8.854 x 10^(-9) C^(2) / Nm^2
R = 0.275mm = 0.000275m
Plugging these values into the equation, we get;
λ = 2π x 8.854 x 10^(-12) x 0.000275 x 5.50 × 10^(6) = 84.14 nC/m
