Question

The filament of an incandescent lamp has a 150 - Ω resistance and carries a direct current of 1.00 A. The filament is 8.00 cm long and 0.900 mm in radius. Calculate the Poynting vector at the surface of the filament, associated with the static electric field producing the current and the current’s static magnetic field.

Answer 1

The Poynting vector at the surface of the filament is determined as 0.416 W/m².

How to calculate the Poynting vector?

The resistivity of the filament is calculated as follows;

R = ρL/A

ρ = RA / L

where;

• R is the resistance
• A is the area
• L is the length

A = πr²

A = π (0.9 x 10⁻³ m )²

A = 2.55 x 10⁻⁶ m²

ρ = RA / L

ρ = (150 x 2.55 x 10⁻⁶ ) / (0.08)

ρ = 4.78 x 10⁻³ Ωm

The current density is calculated as;

J = I/A

J = (1 ) / (2.55 x 10⁻⁶)

J = 3.92 x 10⁵ A/m²

The electric field is calculated as follows;

E = ρJ

E = 4.78 x 10⁻³ Ωm x 3.92 x 10⁵ A/m²

E = 1,873.76 V/m

The magnetic field is calculated as follows;

B = μI/2πr

B = (4π x 10⁻⁷ x 1 A) / (2π x 0.9 x 10⁻³)

B = 2.22 x 10⁻⁴ T

The Poynting vector is calculated as;

S = E × B

S = 1,873.76 V/m × 2.22 x 10⁻⁴ T

S = 0.416 W/m²