Question

The charge per unit length on a long, straight filament is -94.5 µc/m. (a) find the electric field 10.0 cm from the filament, where distances are measured perpendicular to the length of the filament. (take radially inward toward the filament as the positive direction.)

Answer 1

The electric field generated by an uniformly charged wire at a distance r from the wire is given by

`E(r)= (\lambda)/(2 \pi \epsilon _0 r)`
where
`\lambda` is the linear density of charge and
`\epsilon _0 =8.85 \cdot 10^(-12) F/m` is the electric permittivity.
In our problem, the charge density is
`\lambda = -94.5 \mu C/m= -94.5 \cdot 10^(-6) C/m`. We want to calculate the electric field at
`r=10.0 cm=0.1 m`, which is

`E(0.1 m)= (94.5 \cdot 10^(-6) C/m)/(2 \pi (8.85 \cdot 10^(-12) F/m) (0.1 m))=1.7 \cdot 10^7 V/m`
and since the charge on the wire is negative, the field points toward the wire.