Calculate Electric Field at the Center of Semicircular Loop

In summary, the conversation discusses finding the electric field at the center of a semicircular loop of radius a with uniformly distributed charge Q. The hint suggests dividing the loop into charge elements and integrating over the angle theta to find the net field at point P. The conversation also includes a hint on how to write dq in terms of d\theta. Further discussion focuses on using symmetry and setting up the problem in the coordinate plane to find the necessary components of the electric field.
  • #1
kjintonic
11
0
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 don't know how to start this question...
 
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  • #2
kjintonic said:
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 don't know how to start this question...
You must have some idea how to start, have you tried using the hint?
 
  • #3
Probably I can use E= (S)dE= (S)kdq/r^2 inwhich r=a
(S) is integral sign
 
  • #4
kjintonic said:
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 [itex]d\theta[/itex]?

HINT: Notice that the horizontal components will cancel so you need only consider the vertical components of the electric field.
 
  • #5
hmmm... Sorry I kinda don't understant how to write dq in terms of d[itex]d\theta[itex] :(
 
  • #6
bump?
 
  • #7
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 [tex]\lambda dr[/tex], where lambda is Q/length.
 

1. How is the electric field calculated at the center of a semicircular loop?

The electric field at the center of a semicircular loop can be calculated using the equation E = kQ/R, where k is the Coulomb constant, Q is the charge of the loop, and R is the distance from the center of the loop to the point where the electric field is being measured.

2. What is the direction of the electric field at the center of a semicircular loop?

The direction of the electric field at the center of a semicircular loop depends on the orientation of the loop and the charge distribution. In general, the electric field points in the direction of the net force that a positive test charge would experience at that point.

3. How does the radius of the semicircular loop affect the electric field at its center?

The radius of the semicircular loop is a major factor in determining the strength of the electric field at its center. As the radius increases, the electric field decreases, and vice versa. This is because the electric field is inversely proportional to the distance from the center of the loop.

4. Can the electric field at the center of a semicircular loop be negative?

Yes, the electric field at the center of a semicircular loop can be negative if the charge distribution on the loop is asymmetric. This means that the loop has more negative charges on one side and more positive charges on the other. In this case, the electric field would point in the opposite direction of the positive test charge.

5. Are there any real-world applications for calculating the electric field at the center of a semicircular loop?

Yes, there are several real-world applications for this calculation, such as designing electrical circuits, analyzing magnetic fields, and understanding the behavior of charged particles in circular accelerators. It is also used in medical imaging techniques, such as MRI machines, which use magnetic fields to create images of the human body.

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