# Charge density

A semicircular loop of radius a carries positive charge Q distributed uniformly over its length.?
Find the electric field at the center of the loop (point P in the figure). Hint: Divide the loop into charge elements dq as shown in the figure, and write dq in terms of the angle d\theta. Then integrate over \theta to get the net field at P.

http://i533.photobucket.com/albums/ee336/shaneji_kotoba/RW-20-72.jpg

I dunno how to start this question....

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Hootenanny
Staff Emeritus
Gold Member
A semicircular loop of radius a carries positive charge Q distributed uniformly over its length.?
Find the electric field at the center of the loop (point P in the figure). Hint: Divide the loop into charge elements dq as shown in the figure, and write dq in terms of the angle d\theta. Then integrate over \theta to get the net field at P.

http://i533.photobucket.com/albums/ee336/shaneji_kotoba/RW-20-72.jpg

I dunno how to start this question....
You must have some idea how to start, have you tried using the hint?

Probably I can use E= (S)dE= (S)kdq/r^2 inwhich r=a
(S) is integral sign

Hootenanny
Staff Emeritus
Gold Member
Probably I can use E= (S)dE= (S)kdq/r^2 inwhich r=a
(S) is integral sign
You're on the right lines, how about writing dq in terms of $d\theta$?

HINT: Notice that the horizontal components will cancel so you need only consider the vertical components of the electric field.

hmmm... Sorry I kinda don't understant how to write dq in terms of d[itex]d\theta[itex] :(

bump?

Defennder
Homework Helper
First step you should note that by symmetry, one of field components in an axial direction is 0. Now you only have to find the other component. Set this problem up in the coordinate plane with point P at the origin. Draw a triangle for E in terms of E_x and E_y and theta. What can you say about how E_x is related to x? Write down the expression for dE, the differential electric field magnitude due to dq, then try to write dq in terms of $$\lambda dr$$, where lambda is Q/length.