An infinitely long thin straight wire has uniform linear charge density of `(1)/(3) Cm^(-1)` . Then the magnitude of the force acting on a charge `3 mu C` situated at a point of 18 cm away from the wire is
`((1)/(4 pi epsilon_(0))=9 xx 10^(9) Nm^(2)C^(-2))`

Options

A. `2 xx 10^(5) N`
B. `10 ^(5) N`
C. `(1)/(3)xx 10^(6) N`
D. `3 xx 10^(11)N`

Answer

B

Explanation

Given,
Linear charge density , `lambda = (1)/(3) Cm^(-1)`
Charge `q = 3 mu C = 3 xx 10^(-6) C `
Distance ` r = 18 cm = 18 xx 10^(-2) m `
Intensity of the electric field due to infinitely long time at distance r is
`E = (lambda)/(2 pi epsilon_(0)*r) = (2lambda)/(4 pi epsilon_(0)*r)=(9 xx 10^(9) xx 2 xx1)/(3 xx 18 xx 10^(-2))`
`= (1)/(3) xx 10^(11) N//C`
Force on charge of `3 mu C`
F = qE
`= 3 xx 10 ^(-6) xx (1)/(3) xx 10^(11)`
`10 ^(5) N`