Problem : electric field due to line charge

[gracy]

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?

Homework Equations

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]

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]

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.

 

[gracy]

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.

 

[KHram]

Answer is this E=λ/2πε0r
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

 

[Orodruin]

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.