Also Check - Unit, Dimension, Vector Formula
To calculate the magnitude of S, you can use the following formula: |S| = |E| * |B| * sin(θ) Here, |E| is the magnitude of the electric field, |B| is the magnitude of the magnetic field, and θ is the angle between the two fields. Now, let's move on to explore the practical applications of the Poynting Vector.Also Check - Angle Between Two Vectors Formula
Solution 1:
Using the formula |S| = |E| * |B| * sin(θ), we can calculate: |S| = 2 V/m * 1 μT * sin(60°) = 2 * 10^(-6) W/m^2 So, at this point, the magnitude of the Poynting Vector is 2 * 10^(-6) W/m^2. Problem 2: A light wave has an electric field magnitude of 3 V/m and a magnetic field magnitude of 2 μT. Calculate the power transported by this wave through an area of 1 m^2.Solution 2:
The power transported by the wave can be found by multiplying the magnitude of the Poynting Vector by the given area: Power = |S| * A = (3 V/m * 2 μT) * 1 m^2 = 6 * 10^(-6) W The wave transports 6 * 10^(-6) Watts of power through the given area.Also Check - Amplitude Formula
Problem 3: In a certain region, the electric field and magnetic field of an electromagnetic wave are perpendicular to each other. If the magnitude of E is 4 V/m and B is 3 μT, calculate the magnitude of the Poynting Vector.Solution 3:
Since E and B are perpendicular, the angle θ is 90 degrees. Using the Poynting Vector formula: |S| = |E| * |B| * sin(90°) = 4 V/m * 3 μT = 12 * 10^(-6) W/m^2 The magnitude of the Poynting Vector is 12 * 10^(-6) W/m^2. Problem 4: An antenna radiates an electromagnetic wave with an electric field magnitude of 10 V/m and a magnetic field magnitude of 5 μT. Calculate the power radiated per unit area.Solution 4:
Using the Poynting Vector formula, we can calculate the power per unit area: Power = |S| = |E| * |B| = 10 V/m * 5 μT = 50 * 10^(-6) W/m^2 So, the power radiated per unit area is 50 * 10^(-6) W/m^2. Problem 5: A laser beam with an electric field magnitude of 8 V/m and a magnetic field magnitude of 2 μT is used in an optical experiment. Calculate the Poynting Vector magnitude.Solution 5:
Using the Poynting Vector formula: |S| = |E| * |B| = 8 V/m * 2 μT = 16 * 10^(-6) W/m^2 The magnitude of the Poynting Vector for this laser beam is 16 * 10^(-6) W/m^2. These examples demonstrate the practical application of the Poynting Vector Formula in various scenarios. Now, let's address some frequently asked questions about the Poynting Vector.