a- 8.4) Uniform arc A bent semi-circular rod of radius a carries total charge Q uniformly distributed along the rod. Compute the electric field at the origin. la

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a-
8.4) Uniform arc
A bent semi-circular rod of radius a carries total charge Q uniformly
distributed along the rod. Compute the electric field at the origin.
la
Transcribed Image Text:a- 8.4) Uniform arc A bent semi-circular rod of radius a carries total charge Q uniformly distributed along the rod. Compute the electric field at the origin. la
Expert Solution
Examination of the given problem.

The given rod is semicircular in shape, the charges are distributed uniformly along the surface of the rod. the approach will be to calculate the electric field at small distribution, then integrating the distribution for the semicircle.

 

Calculation of the electric field for the small section

consider a small section on the rod as shown in the figure below:

Electrical Engineering homework question answer, step 2, image 1

let the charge distribution density be

Electrical Engineering homework question answer, step 2, image 2

 The charge contained in the small elemental length is given as:
Electrical Engineering homework question answer, step 2, image 3

The electric field at point P  is given as

Electrical Engineering homework question answer, step 2, image 4

 

estimation of the net electric field.

the net electric field is the sum of the horizontal and the vertical electric field. the vertical components will cancel each other while the horizontal component will be present.

Electrical Engineering homework question answer, step 3, image 1

this component will be integrated to find the net electric field.

the value of the

Θ varies from -pi/2 to pi/2

Electrical Engineering homework question answer, step 3, image 2

the above equation can be simplified as:
Electrical Engineering homework question answer, step 3, image 3

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