An infinite line charge produces a field of `9xx10^(-4)N" "C^(-1)` at a distance of 2 cm. calculate the linear charge density.

Options

A. `10^(-3)Cm^(2)`
B. `10^(-4)Cm^(2)`
C. `10^(-5)Cm^(2)`
D. `10^(-7)Cm^(2)`

Answer

D

Explanation

Let `lambda` be the linear charge density.
Electric field due to infinite line charge, `E=(lambda)/(2pi epsilon_(0)r)`. Dividing and multiplying by 2 to get `(1)/(4pi epsilon_(0))`, because we have the value of `(1)/(4pi epsilon)`
`rArr" "E=(2)/(2)xx(lambda)/(2pi epsilon_(0)r)=(2lambda)/(4pi epsilon_(0)r)`
Putting the values, we get
`9xx10^(4)=(2xx9xx10^(9)xxlambda)/(2xx10^(-2))`
`therefore" Linear charge density, "lambda=(9xx10^(4)xx2xx10^(-2))/(2xx9xx10^(9))`
`=10^(-7)Cm^(-1)`
Thus, the linear charge density is `10^(-7)Cm^(-1).`