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
E=k2λ/r
E=9•10⁹•2•87•10⁻⁶/2•0.1 =...
E=9•10⁹•2•87•10⁻⁶/2•0.26 =...
E=9•10⁹•2•87•10⁻⁶/2•1.4 =...
To find the electric field at a certain distance from a long, straight filament with a charge per unit length, you can use the formula for the electric field due to an infinitely long charged wire:
E = (k * λ) / r
Where:
E is the electric field
k is the Coulomb's constant (k = 8.99 x 10^9 Nm^2/C^2)
λ is the charge per unit length of the filament
r is the distance from the filament
(a) For the first question, the distance from the filament is given as 10.0 cm. Convert it to meters by dividing by 100:
r = 10.0 cm/100 = 0.1 m
Substitute the given values into the formula:
E = (8.99 x 10^9 Nm^2/C^2 * (-87.0 x 10^-6 C/m)) / 0.1 m
Calculate the electric field:
E = -7.7963 x 10^4 N/C = -7.80 x 10^4 N/C
Therefore, the electric field 10.0 cm from the filament is -7.80 x 10^4 N/C (You did not provide the unit conversion factor for MN/C to N/C, so I gave the answer in N/C).
(b) Repeat the same process for the second question. The distance from the filament is given as 26.0 cm:
r = 26.0 cm/100 = 0.26 m
Substitute the values into the formula:
E = (8.99 x 10^9 Nm^2/C^2 * (-87.0 x 10^-6 C/m)) / 0.26 m
Calculate the electric field:
E = -2.9385 x 10^4 N/C = -2.94 x 10^4 N/C
Therefore, the electric field 26.0 cm from the filament is -2.94 x 10^4 N/C.
(c) Finally, for the third question, the distance from the filament is given as 140 cm:
r = 140 cm/100 = 1.4 m
Substitute the values into the formula:
E = (8.99 x 10^9 Nm^2/C^2 * (-87.0 x 10^-6 C/m)) / 1.4 m
Calculate the electric field:
E = -5.35 x 10^3 N/C = -5.35 x 10^3 N/C
Therefore, the electric field 140 cm from the filament is -5.35 x 10^3 N/C.
To find the electric field at different distances from the filament, we can use the formula for the electric field produced by a charged filament. The electric field at a distance r from the filament is given by:
E = (k * λ) / r
where E is the electric field, k is Coulomb's constant (9.0 x 10^9 Nm^2/C^2), λ is the charge per unit length, and r is the distance from the filament.
(a) Let's start by finding the electric field 10.0 cm from the filament.
Given:
λ = -87.0 µC/m = -87.0 x 10^-6 C/m (notice the negative sign indicates the charge is negative)
r = 10.0 cm = 10.0 x 10^-2 m
Plugging in the values into the formula:
E = (k * λ) / r
E = (9.0 x 10^9 Nm^2/C^2) * (-87.0 x 10^-6 C/m) / (10.0 x 10^-2 m)
E = -7.0 N/C
Therefore, the electric field 10.0 cm from the filament is -7.0 N/C, directed radially inward towards the filament.
(b) Now, let's find the electric field 26.0 cm from the filament.
Given:
λ = -87.0 µC/m = -87.0 x 10^-6 C/m
r = 26.0 cm = 26.0 x 10^-2 m
Using the same formula:
E = (k * λ) / r
E = (9.0 x 10^9 Nm^2/C^2) * (-87.0 x 10^-6 C/m) / (26.0 x 10^-2 m)
E = -2.663 MN/C
Therefore, the electric field 26.0 cm from the filament is -2.663 MN/C, directed radially inward towards the filament.
(c) Lastly, let's find the electric field 140 cm from the filament.
Given:
λ = -87.0 µC/m = -87.0 x 10^-6 C/m
r = 140 cm = 140 x 10^-2 m
Using the same formula:
E = (k * λ) / r
E = (9.0 x 10^9 Nm^2/C^2) * (-87.0 x 10^-6 C/m) / (140 x 10^-2 m)
E = -5.214 x 10^-6 MN/C
Therefore, the electric field 140 cm from the filament is -5.214 x 10^-6 MN/C, directed radially inward towards the filament.