Question

A strip of invisible tape 0.17 m long by 0.011 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, 0.09, 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.) What is the approximate electric field at A due to piece 1? E rightarrow_l = N/C What is the approximate electric field at A due to piece 2? E rightarrow_2 = N/C What is the approximate electric field at A due to piece 3? E rightarrow_3 = N/C What is the approximate net electric field at A? E rightarrow_net = N/C What could you do to improve the accuracy of your calculation? Use more sections: as the number of segments approaches infinity, the summation of the electric fields approximates the actual electric field. 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.

Please answer in vector format! Thanks!!

Answer 1

a) Charge of the piece = 4/3 *10^-9 C = 1.333e-9 C

distance of the midpoint from origin = 0.17/3 m = 0.0567 m

Electric field at A = kq/r^2

= 9e9*1.333e-9/[0.0567^2 +0.09^2] *0.0567/sqrt[0.0567^2 +0.09^2] i + 9e9*1.333e-9/[0.0567^2 +0.09^2] *0.09/sqrt[0.0567^2 +0.09^2] j

= 565 i + 897j

Hence field is (565, 897, 0) N/C

b) Charge of middle piece = 4/3 *10^-9 C = 1.333e-9 C

distance of the midpoint from origin = 0 m

Electric field at A = kq/r^2

= 9e9*1.333e-9/[ 0.09^2]

=1481 j N/C

Hence field is (0, 1481, 0) N/C

part c) because of symmetrical to part a

E =  (-565, 897, 0) N/C

part d) Enet= [(565+0-565), (897+1481+897) , 0]

=  [ 0 , 3275 , 0 ] N/C