## DLS 2 years ago Derive an expression for the G.field due to a uniform rod of Length L and mass M at a point on its perpendicular bisector at a distance d from the centre

1. DLS

|dw:1361012885773:dw|

2. DLS

$\LARGE \frac{2GM}{\sqrt{4L^2+d^2}}$ is what I got one term seems missing

3. yrelhan4

again, seems like you didnt take the components right. E will be given by dE= 2dE1 sintheta where dE1=G(dm)/(d^2 + x^2) where dm=m/l dx sintheta=d/(d^2 + x^2) integrate with respect to x from 0 to l/2 |dw:1361012228614:dw|

4. Mashy

lol.. in such cases its better to take 2 diametrically opposite mass elements!

5. DLS

??

6. Mashy

wait wait..lemme think!

7. yrelhan4

@DLS you didnt get what i said?

8. DLS

no ..u wrote scary symbols :P

9. yrelhan4

hmm. haha :P

10. Mashy

|dw:1361026132081:dw| something liek this??.. cause if you consider two elements at a time, then the net field due to them becomes perpendicular to the rod.. and hence you can now add up all the elements.. else you couldn't add up directly.. cause, the fields would be in different directions!

11. Mashy

|dw:1361026342375:dw|

12. DLS

ek se kyun nahi kar sakte O.O

13. DLS

|dw:1361026384089:dw|

14. Mashy

you need to learn more vector analysis.. its a continous mass distribution!..

15. DLS

:/ what

16. Mashy

yrelhan please explain.. dls whatever he said .. is exactly correct!

17. DLS

bolo na :/

18. yrelhan4

what should i explain?

19. yrelhan4

ek se kyu nhi kr skte? in these kind of questions we always take 2 elements so that1 component cancel out and we are left with one. easier to integrate. how to do with one element? i dont know.

20. Vincent-Lyon.Fr

You can integrate more easily using an angular variable.

21. abb0t

Can't you use similar triangles?

22. Vincent-Lyon.Fr

I have: $$\LARGE \frac{2GM}{d\sqrt{L^2+4d^2}}$$

23. DLS

i didnt get d :/

24. DLS

i mean whats wrong with my method

25. DLS

The mass is a distance of $\LARGE \sqrt{L^2+\frac{d^2}{4}}$ from the rod

26. Vincent-Lyon.Fr

???? the mass is a distance $$\Large d$$ from the rod. What is your method? I have not seen it in your posts.

27. Vincent-Lyon.Fr

It's like a problem of electric field. You have to integrate Newton's law of universal gravitation in the same way as you would use Coulomb's law for charges.

28. DLS

so cant we do like this integrate from $\LARGE \sqrt{L^2+\frac{d^2}{4}}$ to L/2 and multiply it by 2 :O

29. DLS

that would be complicated but eh

30. DLS

why are we considering elemental mass?

31. Vincent-Lyon.Fr

This is why I told you to use angle as integration variable.

32. DLS

okay..thanks :O but thats correct right?just complex..thanks!

33. Vincent-Lyon.Fr

Wait, I'll send the derivation.

34. Vincent-Lyon.Fr

Here it is.