Question

A plastic rod 1.6 m long is rubbed all over with wool, and acquires a charge of -9e-08 coulombs. We choose the center of the rod to be the origin of our coordinate system, with the x-axis extending to the right, the y-axis extending up, and the z-axis out of the page. In order to calculate the electric field at location A = < 0.7, 0, 0 > m, we divide the rod into 8 pieces, and approximate each piece as a point charge located at the center of the piece.

Answer 1

Solution :

Length of the plastic rod , L = 1.6 m

Total charge on the plastic rod , Q = $-9 \times 10^{-8}$ C

The rod is divided into 8 pieces.

a). The length of the 8 pieces is , $l=\frac{L}{8}$

                                                         $=\frac{1.6}{8}$

                                                         = 0.2 m

b). Location of the center of the piece number 5 is given as : 0 m, -0.09375 m, 0 m.

c). The charge q on the piece number 5 is given as

$q=\frac{Q}{L}\times l$

$q=\frac{-9 \times 10^{-8}}{1.6}\times0.2$

 = $-1.125 \times 10^{-8}$ C

d). WE approximate that piece 5 as a point charge and we need to find out the field at point A(0.7 m, 0, 0) only due to the charge.

We know,  the Coulombs force constant, k = $8.99 \times 10^9 \ N.m^2/C^2$

So the X component of the electric field at the point A  is given as

$E_x = 8.99 \times 10^9 \times 1 \times 10^{-8} \ \cos \frac{187.628}{0.70625}$

     = -126.15 N/C

The Y component of the electric field at the point A is

$E_y = 8.99 \times 10^9 \times 1 \times 10^{-8} \ \sin \frac{187.628}{0.70625}$

    = -16.93 N/C

Now since the rod and the point A is in the x - y plane, the z component of the field at point A due to the piece 5 will be zero.

∴ $E_z=0$

Thus, $E=$