Homework Help: Problem : electric field due to line charge

1. Sep 15, 2015

gracy

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

E=λ/2πε0r
3. 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?

2. Sep 15, 2015

Orodruin

Staff Emeritus
λ is the charge per unit length on the rod, not the total charge of the rod.

3. Sep 16, 2015

gracy

But there is λ in formula not total charge.

4. Sep 16, 2015

haruspex

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.

5. Sep 16, 2015

gracy

oh!yes,sorry.

6. Dec 29, 2017

KHram

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

7. Dec 30, 2017

Orodruin

Staff Emeritus
This thread is two years old and the OP already had the correct formula, just not the correct understanding of it.

Also, please remember the PF rules against posting full solutions.