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 a given distance from a long, straight filament with a charge per unit length, you can use the formula for the electric field due to a line charge. The formula is given as:
E = (k * λ) / r
Where:
E is the electric field
k is the Coulomb's constant (9.0 x 10^9 N m^2/C^2)
λ is the charge per unit length
r is the distance from the filament
Now, let's apply this formula to the given distances:
(a) Find the electric field 10.0 cm from the filament.
First, we need to convert the charge per unit length from microCoulombs per meter to Coulombs per meter:
λ = -87.0 µC/m = -87.0 x 10^-6 C/m
Now, we can calculate the electric field:
E = (k * λ) / r
E = (9.0 x 10^9 N m^2/C^2) * (-87.0 x 10^-6 C/m) / (10.0 x 10^-2 m)
E = (-783 x 10^3 N/C) / (0.1 m)
E = -7.83 x 10^6 N/C
E = -7.83 MN/C (Answer)
(b) Find the electric field 26.0 cm from the filament.
Again, convert the charge per unit length to Coulombs per meter:
λ = -87.0 µC/m = -87.0 x 10^-6 C/m
Calculate the electric field:
E = (k * λ) / r
E = (9.0 x 10^9 N m^2/C^2) * (-87.0 x 10^-6 C/m) / (26.0 x 10^-2 m)
E = (-783 x 10^3 N/C) / (0.26 m)
E = -3.01 x 10^6 N/C
E = -3.01 MN/C (Answer)
(c) Find the electric field 140 cm from the filament.
Once again, convert the charge per unit length to Coulombs per meter:
λ = -87.0 µC/m = -87.0 x 10^-6 C/m
Calculate the electric field:
E = (k * λ) / r
E = (9.0 x 10^9 N m^2/C^2) * (-87.0 x 10^-6 C/m) / (140 x 10^-2 m)
E = (-783 x 10^3 N/C) / (1.4 m)
E = -5.59 x 10^5 N/C
E = -0.559 MN/C (Answer)
Hence, the electric fields are:
(a) -7.83 MN/C
(b) -3.01 MN/C
(c) -0.559 MN/C