What electric field strength would store 17.5J of energy in every 9.00mm3 of space?
To find the electric field strength that would store 17.5 J of energy in every 9.00 mm^3 of space, we can use the formula:
Electric Field Strength (E) = √(2 * Energy Density / Permittivity of Free Space)
Given:
Energy Density = 17.5 J
Volume (V) = 9.00 mm^3
Permittivity of Free Space (ε0) = 8.854 x 10^-12 C^2 / (N * m^2)
Step 1: Convert the volume to cubic meters
1 mm^3 is equal to (1 x 10^-9) m^3
So, the volume in cubic meters (V_m) is:
V_m = V * (1 x 10^-9) m^3
= 9.00 mm^3 * (1 x 10^-9) m^3
= 9.00 x 10^-18 m^3
Step 2: Calculate the Energy Density per unit volume (U)
U = Energy Density / Volume
= 17.5 J / (9.00 x 10^-18 m^3)
= 1.94 x 10^18 J/m^3
Step 3: Calculate the Electric Field Strength (E)
E = √(2 * U / ε0)
= √(2 * 1.94 x 10^18 J/m^3 / (8.854 x 10^-12 C^2 / (N * m^2)))
= √((2 * 1.94 x 10^18 J/m^3) * (8.854 x 10^-12 N * m^2 / C^2))
= √(3.43 x 10^7 N/m^2)
≈ 5868 N/C
Therefore, the electric field strength that would store 17.5 J of energy in every 9.00 mm^3 of space is approximately 5868 N/C.
To determine the electric field strength that would store 17.5J of energy in every 9.00mm³ of space, you need to use the formula for electric potential energy.
The formula for electric potential energy is given by:
U = (1/2)ε₀E²V,
where U is the electric potential energy, ε₀ is the vacuum permittivity (ε₀ ≈ 8.85 x 10⁻¹² F/m), E is the electric field strength, and V is the volume of space.
We can rearrange the formula to solve for E:
E = √(2U/(ε₀V)).
Now, substitute the given values:
U = 17.5J,
V = 9.00mm³ = (9.00 x 10⁻³ cm)³.
First, convert the volume to meters:
V = (9.00 x 10⁻³ cm)³ = (9.00 x 10⁻⁵ m)³ = 7.29 x 10⁻¹⁵ m³.
Now, substitute the values into the formula to calculate E:
E = √(2(17.5J)/((8.85 x 10⁻¹² F/m)(7.29 x 10⁻¹⁵ m³))).
Calculating this expression will give you the electric field strength in units of volts per meter (V/m).
energy density= 1/2 epsilion abs(E^2)
9 mm^3=9 (1m/E3 mm)^3=9E-9 m^3
energy density= 17/8E-9= 2.125E9 J/m^3
now solve for E