What is the charge inside a positively charged solid nonconducting cylinder with given parameters?
What is the charge inside the cylinder?
The charge inside the cylinder is 15.81 N/C.
Calculation of Charge Inside the Cylinder
A positively charged solid nonconducting cylinder has the following parameters:
- Length (ℓ) = 10 m
- Radius (R) = 50 mm = 50 x 10^-3 m
- Volume charge density (ρ) = + 7.0 × 10^−9 C/m^3
The charge inside the cylinder can be calculated using the formula: Q = ρV
Where:
- V = Volume of the cylinder
- V = πR^2ℓ
- V = 3.1415 x (50x10^-3)^2 x 10
- V = 78.53 x10^-3 m^3
Therefore, substituting the values into the formula, we get:
Q = (+ 7.0 × 10^−9 C/m^3) x (78.53 x10^-3 m^3)
Q = 5.4971 x10^-10 C
What is the electric field magnitude at a radial distance of 40 mm from the central axis of the cylinder?
The electric field magnitude at r = 40 mm is 15.81 N/C.
Calculation of Electric Field Magnitude
To calculate the electric field magnitude at a radial distance r = 40 mm from the central axis of the cylinder, we use the formula: E = ρr/ε₀
Given parameters:
- Permitivity of free space (ε₀) = 8.85 x10^-12 C^2/Nm^2
- Radial distance (r) = 40 mm = 40 x10^-3 m
Substitute the values into the formula:
E = (7 x10^-9 )(40x10^-3 ) / (2 x 8.85 x10^-12 )
E = 15.81 N/C