Calculate Electric Field at Origin 0 - $\lambda, \vartheta, R$

[afm-91]

l need your help !

A thin rod bent into the shape of an arc of a circle of radius R carries a uniform charge per unit length$$\lambda$$ . The arc subtends a total angle2$$\vartheta$$ , symmetric about the X axis, as shown in the figure.

Determine the magnitudeE of the electric field at the origin 0??

Express your answer in terms of the variables $$\lambda$$, $$\vartheta$$,R , and appropriate constants.






Determine the direction of the electric field E at the origin 0.?
to the left
to the right

 

[Redbelly98]

Welcome to PF

The way this forum works is, the student posts the relevant equation(s) and makes an attempt at solving the problem before getting help. Even if that attempt is wrong, we like to know you have put some thought into the problem.

Your textbook should have an equation for getting the field of an extended charge (i.e., not point charges). Try finding that equation, and think about how it can be applied here.

 

[afm-91]

E = k$$\lambda$$/R
?

TODAY IS THE LAST DAY FOR THE HOME WORK >>> PLZ HELP ME !

 

[afm-91]

no body can help me?

 

[Redbelly98]

E = k$$\lambda$$/R
?

Not quite. That is for a straight, infinitely long rod or wire.

This one will require integrating,

$$\stackrel{\rightarrow}{E} \ = \int\frac{k \ \hat{r}}{r^2} \ \lambda \ dl$$

A couple of questions for you:
Have you had calculus?
Is there an example worked out in your textbook or class lecture notes, where they do an integral similar to the above equation?

TODAY IS THE LAST DAY FOR THE HOME WORK >>> PLZ HELP ME !

I'll help as I can, but I am not constantly on the computer all the time today.

 

[afm-91]

how can i solve this integral??

 

[Redbelly98]

There really should be an example worked out in your book.

You'll need to decide which terms in the integral are constants, and which are variables. Also, the fact that E is a vector, and that "r-hat" can change direction, must be taken into account.

 

[CompuChip]

Redbelly, I'm afraid it is too late anyway.

Perhaps it is a good idea to try and start working on your problems a bit longer than one day before the deadline. Learning physics is not like learning history: it requires understanding more than learning stuff by heart, and that takes time.