The charge per unit length on a long, straight filament is -87.0 µC/m.
(a) Find the electric field 10.0 cm from the filament. Distances are measured perpendicular to the length of the filament. (Take radially inward toward the filament as the positive direction.)
MN/C
(b) Find the electric field 26.0 cm from the filament.
MN/C
(c) Find the electric field 140 cm from the filament.
MN/C
To find the electric field at different distances from the filament, we can use the formula for the electric field due to a straight filament:
E = (k * λ) / r
Where:
E is the electric field
k is the Coulomb's constant (9.0 x 10^9 Nm^2/C^2)
λ is the charge per unit length on the filament
r is the distance from the filament
(a) To find the electric field 10.0 cm from the filament:
First, convert the charge per unit length from µC/m to C/m:
λ = -87.0 µC/m = -87.0 x 10^(-6) C/m
Next, convert the distance from cm to m:
r = 10.0 cm = 10.0 x 10^(-2) m
Now, substitute the values into the formula:
E = (9.0 x 10^9 Nm^2/C^2) * (-87.0 x 10^(-6) C/m) / (10.0 x 10^(-2) m)
Calculate the expression to find the electric field.
(b) To find the electric field 26.0 cm from the filament:
Follow the same steps as in part (a), using a new distance value for r.
(c) To find the electric field 140 cm from the filament:
Repeat the steps again, using a new distance value for r.
By following these steps and performing the necessary calculations, you can find the electric fields at the different distances from the filament.