A strip of invisible tape 0.19 m long by 0.017 m wide is charged uniformly with

Question

A strip of invisible tape 0.19 m long by 0.017 m wide is charged uniformly with a total net charge of 4 nC (nano = 1 times 10^-9) and is suspended horizontally, so it lies along the x axis, with its center at the origin, as shown in the figure below. Calculate the approximate electric field at location (0, 0.07, 0) m (location A) due to the strip of tape. Do this by dividing the strip into three equal sections, as shown in the figure below, and approximating each section as a point charge. (Assume each point charge is located at the center of the section it approximates. Express your answer in vector form.) (a) What is the approximate electric field at A due to piece 1? E_1 = N/C (b) What is the approximate electric field at A due to piece 2? E_2 = N/C (c) What is the approximate electric field at A due to piece 3? E_3 = N/C (d) What is the approximate net electric field at A? E_net = N/C (e) What could you do to improve the accuracy of your calculation? Use a larger charge for piece 2 than for pieces 1 and 3: since location A is closest to piece 2, this piece has the most significant contribution. Use a smaller charge for piece 2 than for pieces 1 and 3: the actual electric field is similar to the field of a dipole, with most of the charge on the tape at the left and right ends. Use just two sections: due to symmetry about the y-axis, the components of the field due to each charge will be half of the total electric field.

Explanation / Answer

let's satrt with identifying the center of each strip,

Each strip will be ( 0.19/ 3 x 0.017) = ( 0.063 x 0.017)

The center of strip 1 will lie at ( -0.0633, 0) , center of second strip ( 0.0) , while the center of strip 3( + 0.0633, 0)

Distance between strip 1 and test point = sqroot ( 0.0633^2 + 0.07^2) = 0.094 m apprx

E( due to strip 1) = 9 x 10^9 ( 1.33 x 10^-9)/ ( 0.094 )^2 = 1358 N/C aprx

E( due to strp 2) =  9 x 10^9 ( 1.33 x 10^-9)/ (0.07)^2 = 2448 . 979 N/C apprx

E( due to strip 3) = 1358 N/C

E1 and E2 will have only y components while x components will cancel due to symmetry.. Angle between center of strp 1 and point = tan^-1 ( 0.07/ 0,0633) = 47.877 degree apprx

Net electric field at point = 2 (1358) sin 47.877 +2448 . 9798= 4463. 454 N/C apprx

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