Question

A straight, nonconducting plastic wire 7.50cm long carries a charge density of 130nC/m distributed uniformly along its length. It is lying on a horizontal tabletop. Part C If the wire is now bent into a circle lying flat on the table, find the magnitude and direction of the electric field it produces at a point 5.00cm directly above its center.

Answer 1

Find the magnitude and direction of the electric field this wire produces at a point 5.00 cm directly above its midpoint.
Draw a Gaussian surface which may be a hollow cylinder with the rod at its central
axis. Then apply Gauss's law:

E = Q/2?r?oL = ?L/2?rL = ?/2??or

E = 175x10^-9/[2?(0.06)8.75x10^-12 = 5.24x10^4 N/C

Due to symmetry the horizonal component of the field cancel each other.

Therefore, only the vertical component of the field exist.

(Ey) = Esin?,

? = arctan{r/(L/2) = arctan{2*0.06/0.075} = arctan{1.41} = 54.69 deg.

(Ey) = (5.24x10^4)sin54.69 = (5.24x10^4)0.816 = 4.28x10^4 N/C

If the wire is now bent into a circle lying flat on the table, find the magnitude and direction of the electric field it produces at a point 5.00 cm directly above its center.


L = 2?r, => r = L/2? = 0.075/2? = 0.0135 m

d = ? (r