Purchase Solution

Electrostatic Field and Potential

Not what you're looking for?

Ask Custom Question

I would appreciate help in completing the proof of the equation on the
second line of the attached file.

Attachments
Purchase this Solution
Solution Summary

The electrostatic field and potentials are determined. A detailed solution is given.

Solution Preview

What you need to prove is not that div[phi E] = 0, but rather that div[phi E] integrated over a volume approaches zero in the limit that the volume becomes infinitely large. If div[phi E] were a positive definite quantity then this would also imply that div[phi E] = 0 everywhere, but it isn't! div[phi E] can be negative or positive.

I'm now going to derive the result step by step.

Consider the volume integral:

Volume integral [rho phi].

Replacing rho = epsilon_0 div E ...

Purchase this Solution
Free BrainMass Quizzes
Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

The Moon

Test your knowledge of moon phases and movement.

Basic Physics

This quiz will test your knowledge about basic Physics.

View More Free Quizzes
Related BrainMass Solutions

  • Equilibrium between gravity and electrostatic field

    This solution determines the equilibrium between gravity and an electrostatic field.

  • Electrostatic Field and Potential in Spheres

    505150 Electrostatic Field and Potential in Spheres See the attached file. 1. The electrostatic field E in a particular region can be expressed in terms of spherical coordinates. Derive an expression for the potential difference. 2.

  • Potential Energies

    However, a STATIC electric field is indeed POTENTIAL, and this is the reason one should strictly speaking say "electrostatic potential" or "electrostatic potential energy".

  • Electrostatic Potential

    512631 Electrostatic Potential Another illustration of the use of Legendre polynomials is provided by the problem of a neutral conducting sphere (radius r_0) placed in a (previously) uniform electric field (see attachment).

  • Work done to assemble the four charges together

    103780 Impossible electrostatic field, charges and work See attached file for full problem description. 8.

  • Four charges are placed at the corners of a square, where q is positive

    If two diagonal charges have the same magnitude and sign, then the electric field at the center due to these two charges have equal magnitude and opposite directions. Their resultant is, therefore, zero.

  • Physics: Electrostatics

    410836 Electrostatic potential energy, force and electric field intensity. 1. A -3 micro C charge is placed 6 mm away from a -9 micro C charge. What is the potential energy in Joules? 2.

  • Electrostatics and potential differences

    After the electron has moved 3.20 cm, what is (a) the work done by the field on the electron, (b) the change in potential energy associated with the electron, and (c) the velocity of the electron?

  • Electrostatics and calculation is related to electric field and potential.

    The electrostatic calculations as they relate the the electric field and potentials are provided. An expression for the electric field is provided.

  • Electric Potential

    is defined as: Where is the electric field vector in space, and d is the line segment vector.

View More Related Solutions