150 pJ of energy is stored in a 1.0 cm times 1.0 cm times 1.0 cm region of uniform electric field.
What is the electric field strength?
Energy stored in E-field =
(1/2)*(epsilono)*E^2*(Volume)
Make sure the volume is in m^3.
You have been given the energy, so solve for E
Well, if you want to know the electric field strength, you've come to the right place! Let's do some calculations, with a little bit of clowning around, of course.
To find the electric field strength, we need to divide the amount of energy stored by the volume of the region. So, we would have:
Energy = Electric field strength × Volume
Given that the energy is 150 pJ and the volume is 1.0 cm × 1.0 cm × 1.0 cm (which is just 1 cm³), we have:
150 pJ = Electric field strength × 1 cm³
Now, let's bring those units into a more manageable form. We'll convert the picajoules (pJ) to joules (J) and the cubic centimeters (cm³) to cubic meters (m³), just to keep things consistent.
1 pJ = 1 × 10⁻¹² J
1 cm³ = 1 × 10⁻⁶ m³
So, plugging those values in, we have:
150 × 10⁻¹² J = Electric field strength × 1 × 10⁻⁶ m³
Now, let's solve for the electric field strength. Dividing both sides of the equation by 1 × 10⁻⁶ m³, we get:
Electric field strength = (150 × 10⁻¹² J) / (1 × 10⁻⁶ m³)
Simplifying further, we get:
Electric field strength = 150 × 10⁻⁶ / 1 = 150 × 10⁻⁶ N/m
So, the electric field strength is 150 μN/m. Remember, this is all just clowning around, but I hope it helps!
To find the electric field strength, we need to use the equation:
Energy = Electric field strength × Volume
Given:
Energy (E) = 150 pJ = 150 × 10^(-12) J
Volume (V) = 1.0 cm × 1.0 cm × 1.0 cm = 1 cm^3
We can rearrange the equation to solve for the electric field strength (E-field):
E-field = Energy / Volume
Substituting the values:
E-field = (150 × 10^(-12) J) / (1 cm^3)
Now, we need to convert the volume from cm^3 to m^3, as the SI unit of energy is J and the SI unit of volume is m^3.
1 cm^3 = (1 × 10^(-2) m)^3 = 1 × 10^(-6) m^3
E-field = (150 × 10^(-12) J) / (1 × 10^(-6) m^3)
Simplifying:
E-field = 150 × 10^(-12) / 10^(-6)
E-field = 150 × 10^(-12+6)
E-field = 150 × 10^(-6) = 150 μN/C
Therefore, the electric field strength is 150 μN/C.
To find the electric field strength, we can use the formula:
E = √(2E / ε₀V)
where:
E is the energy stored in the electric field
ε₀ is the permittivity of free space
V is the volume of the region of uniform electric field
In this case, we are given E (150 pJ) and V (1.0 cm x 1.0 cm x 1.0 cm). However, we need to determine the value of ε₀.
The permittivity of free space (ε₀) is a fundamental constant that describes the properties of electric fields. It is approximately equal to 8.854 x 10^(-12) C²/Nm².
Plugging in the values into the formula, we have:
E = √(2 * (150 pJ) / (8.854 x 10^(-12) C²/Nm² * (1.0 cm x 1.0 cm x 1.0 cm)))
Now let's convert the units to the appropriate SI units:
1 pJ = 10^(-12) J
1 cm = 10^(-2) m
E = √(2 * (150 x 10^(-12) J) / (8.854 x 10^(-12) C²/Nm² * (1.0 x 10^(-2) m x 1.0 x 10^(-2) m x 1.0 x 10^(-2) m)))
E = √(2 * 150 * 10^(-12) / (8.854 x 10^(-12) * 10^(-4) * 10^(-4) * 10^(-4))) N/C
Simplifying the expression:
E = √(2 * 150 * 10^(-12) / (8.854 x 10^(-12) * 10^(-12))) N/C
E = √(2 * 150 / 8.854) N/C
E = √(337.2) N/C
E ≈ 18.35 N/C
Therefore, the electric field strength is approximately 18.35 N/C.