# Problem : electric field due to line charge

## Homework Statement

A non conducting rod of length 2.2 m carries a negative charge of 3.8 ×10^-7 spread uniformly over it's length .What is the magnitude of electric field near the mid point of the rod at a perpendicular distance 3.6 mm from the rod?

E=λ/2πε0r

## The Attempt at a Solution

As it has been given that we have to calculate electric field near the mid point of the rod ;we can use the formula of infinite line charge for our rod of finite length (i.e 2.2m)
using formula
E=λ/2πε0r
E=2λ/ 4πε0r
PUTTING VALUES
=9 ×10^9 ×2 ×3.8 ×10^-7/3.6 ×10^-3
=19 ×10^5 N/C
but the answer should be 8.6 ×10^5 N/C
where I am getting wrong?

Orodruin
Staff Emeritus
Homework Helper
Gold Member
λ is the charge per unit length on the rod, not the total charge of the rod.

gracy
λ is the charge per unit length on the rod, not the total charge of the rod.
But there is λ in formula not total charge.
E=λ/2πε0r

haruspex
Homework Helper
Gold Member
2020 Award
But there is λ in formula not total charge.
I don't understand what you are trying to say. As Orodruin posted, the lambda in the formula you quote represents the charge per unit length. To use the formula, you must first calculate that from the given charge and length information.

I don't understand what you are trying to say. As Orodruin posted, the lambda in the formula you quote represents the charge per unit length. To use the formula, you must first calculate that from the given charge and length information.
oh!yes,sorry.

λ=unit charge =total charge÷length
=3.8×10^7/2.2=1.7×10^-7
Now putting all values in formula you wipl get answer 8.6×10^5N/C

Delta2
Orodruin
Staff Emeritus