Understanding Divergence Concepts

What is the mathematical definition of divergence in electric fields?

• Divergence of an electric field is defined as div(E) = ∇ · E.

• Divergence of an electric field is calculated as div(E) = ∇ + E.

• Divergence of an electric field is the rate of change of electric potential.

• Divergence of an electric field is defined as curl(E) = ∇ × E.

How does the divergence of an electric field relate to charge density?

• The divergence of an electric field is inversely proportional to charge density.

• The divergence of an electric field is proportional to charge density.

• The divergence of an electric field is equal to the square of charge density.

• The divergence of an electric field is independent of charge density.

Calculate the divergence of the vector field F(x, y, z) = (x^2, y^2, z^2).

• 2x + 2y

• x^2 + y^2 + z^2

• 3x + 3y + 3z

• 2x + 2y + 2z

What is the physical significance of a positive divergence in a vector field?

• A positive divergence indicates a sink in the vector field.

• A positive divergence represents uniform flow in the vector field.

• A positive divergence signifies a source in the vector field.

• A positive divergence shows no change in the vector field.

What does it mean if the divergence of a vector field is zero?

• The vector field is expanding.

• The vector field is rotational.

• The vector field has a constant magnitude.

• The vector field is incompressible.

In vector calculus, how is divergence represented in terms of partial derivatives?

• div F = ∂F1/∂x + ∂F2/∂x + ∂F3/∂x

• div F = ∂F1/∂x + ∂F2/∂y + ∂F3/∂z

• div F = ∂F1/∂y + ∂F2/∂z + ∂F3/∂x

• div F = ∂F1/∂z + ∂F2/∂y + ∂F3/∂y

How can divergence be interpreted in the context of electromagnetic fields?

• Divergence measures the strength of magnetic fields only.

• Divergence is irrelevant in electromagnetic theory.

• Divergence indicates sources or sinks of electric fields and is zero for magnetic fields.

• Divergence is always positive for electric fields.

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