A rod of length 2.4 m and radius 4.6 mm carries a negative charge of `4.2xx10^(-7)C` spread uniformly over it surface. The electric field near the mid-point of the rod, at a point on its surface is

Options

A. `-8.6xx10^(5)NC^(-1)`
B. `8.6xx10^(4)NC^(-1)`
C. `-6.7xx10^(5)NC^(-1)`
D. `6.7xx10^(4)NC^(-1)`

Answer

C

Explanation

Here, `l=2.4m,r=4.6mm=4.6xx10^(-3)m`
`q=-4.2xx10^(-7)C`
Linear charge density, `lamda=q/l=(-4.2xx10^(-7))/2.4=-1.75xx10^(-7)Cm^(-1)`
Electric field,
`E=lamda/(2piepsilon_(0)r)=(-1.75xx10^(-7))/(2xx3.14xx8.854xx10^(-12)xx4.6xx10^(-3))`
`=-6.7xx10^(5)NC^(-1)`