If E is an electric field and B is the magnetic induction then the energy flow per unit area per unit time in an electromagnetic field is given by

Options

A. `E xxB`
B. E-B
C. `E^(2)+B^(2)`
D. E/B

Answer

To solve the problem of determining the energy flow per unit area per unit time in an electromagnetic field given the electric field \( E \) and the magnetic induction \( B \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept**: In electromagnetic theory, the energy flow per unit area per unit time is represented by the Poynting vector \( \vec{S} \). The Poynting vector describes the directional energy flux (the rate of energy transfer per unit area) of an electromagnetic field.

2. **Formula for the Poynting Vector**: The Poynting vector \( \vec{S} \) is given by the formula:
\[ \vec{S} = \frac{1}{\mu_0} \vec{E} \times \vec{B} \]
where \( \mu_0 \) is the permeability of free space, \( \vec{E} \) is the electric field vector, and \( \vec{B} \) is the magnetic induction vector.

3. **Identify the Cross Product**: The term \( \vec{E} \times \vec{B} \) represents the cross product of the electric field and the magnetic induction. The result of this cross product is a vector that is perpendicular to both \( \vec{E} \) and \( \vec{B} \).

4. **Conclusion**: Thus, the energy flow per unit area per unit time in an electromagnetic field is represented by the Poynting vector \( \vec{S} \), which can be expressed as:
\[ \vec{S} = \frac{1}{\mu_0} \vec{E} \times \vec{B} \]

5. **Select the Correct Option**: From the options provided (E cross B, E minus B, E square plus B square, or E by B), the correct answer is \( \vec{E} \times \vec{B} \). However, since the question does not provide \( \frac{1}{\mu_0} \) as an option, we conclude that the answer is not listed among the options.

### Final Answer:
The energy flow per unit area per unit time in an electromagnetic field is given by \( \vec{S} = \frac{1}{\mu_0} \vec{E} \times \vec{B} \). None of the provided options are correct.