Electric Field on finite charged rod

[n0va]

Homework Statement

Thin rod AB has length L=100 cm and total charge q0=37 nC that is distributed in such a way that its line density $\lambda$ is proportional to the square of the distance from the end A, i.e. $\lambda$(x) =kx^2. Determine electric field E at the end A of the rod.

Homework Equations

E = (1/(4pi$\epsilon$0))
Electric Field for a thin uniformly charged conducting wire: E = $\lambda$/(2$\pi$r$\epsilon$0)

The Attempt at a Solution

if $\lambda$(x) =kx^2 , can we find k by plugging in 1m in x and setting it equal to 37. meaning k is 37.

Since they are asking for the E at point A, is x just 0? and does that mean that E is 0?

 

[n0va]

Does my answer make any sense at all? Or am i misinterpreting it? They're asking for the E field on point A, and since the distribution starts at A, x at that point is 0 and therefore there is no electricfield at point A?

 

[n0va]

Cmon seriously?

 

[SammyS]

Hello n0va.

Welcome to Physics Forums (PF).

Did you read the https://www.physicsforums.com/showthread.php?t=94379", particularly #3 in this case.

To find k, you must integrate over the length of the charged rod & solve for k.$$Q=\int_{0m}^{1m}{kx^2}\,dx$$

The formula you used to find E gives the E field at a distance, r, from an infinitely long charged rod which has uniform linear charge density.

To do this problem, you will have to do an integration over the length of the rod.

 

[ehild]

I suggest you to reread your posts before you send them and check the validity of your statements.

Homework Equations

E = (1/(4pi$\epsilon$0))

What is E? If it denotes the electric field strength how can it be the same for all situations?

Electric Field for a thin uniformly charged conducting wire: E = $\lambda$/(2$\pi$r$\epsilon$0)

This formula is valid for an infinite uniformly charged wire, at a distance r from it. The wire in the problem is neither infinite nor uniformly charged and the field is asked at zero distance from it, at one end.

The Attempt at a Solution

if $\lambda$(x) =kx^2 , can we find k by plugging in 1m in x and setting it equal to 37. meaning k is 37.

No, it is not right. The total charge is given. The integral of the charge density along the wire length is equal to the total charge, 37 nC, as SammyS suggested.

Since they are asking for the E at point A, is x just 0? and does that mean that E is 0?

The electric field has some contribution for all parts of the wire.

ehild