Electrostatics and Magnetostatics
To test the understanding of the lesson
Question
What is the potential electrostatic interaction energy of a charge placed at a point where an electric potential exists ?
What is the potential electrostatic interaction energy of charges , placed at points where an electric potential exists ?
Hint
Solution

The potential electrostatic energy of a charge placed at a point where exists an electric potential is :

The potential electrostatic energy of charges placed at points where exists a potential is :
Question
Define the .
Hint
Solution
The is an energy unit. It is the kinetic energy gained by an electron which was accelerated by a voltage difference . Thus :
Question
What is the potential electrostatic interaction energy of an electric dipole, which has a dipole moment vector surrounded by an exterior uniform field ?
What is the potential magnetic interaction energy of a magnetic dipole, which has a magnetic moment vector surrounded by an exterior uniform magnetic field ?
Hint
Solution

The potential electrostatic interaction energy of an electric dipole, which has a dipole moment vector surrounded by an exterior uniform field is :

The potential magnetic interaction energy of a magnetic dipole, which has a magnetic moment vector surrounded by an exterior uniform magnetic field is :
Question
Define the electric dipole moment of a set of two charges in P and in N.
Define the magnetic moment of a circuit crossed by an intensity . What if the circuit is a circular loop of radius ?
Hint
Solution

The dipole moment is expressed by :

The magnetic moment is :
Where is the circuit surface and the normal vector of the oriented circuit (obtained with the Righthand rule).
For a circular loop whose normal axis is (Oz) for example :
Question
What is the expression of a potential created by a dipole, under the dipole approximation ?
Deduce the electric field created by the dipole.
Hint
Solution

The potential created by the dipole is :

The electric field is given by :
Question
Quote Gauss' law.
Quote Ampère's circuital law.
Hint
Solution

Gauss' law :

Ampère's circuital law :
Question
Eight identical spherical drops of mercury are charged to a voltage equal to .
What will be the voltage of the big drop obtained after the fusion of these drops ?
Hint
Solution
The charge of the initial drop is , with and each drop has a radius equal to .
The big drop has the same volume as the sum of the eight others. Thus its radius is :
Consequently :
Hence the final potential is expressed by :
Question
A nucleus of Neon is accelerated by a voltage difference equal to .
Find its velocity, considering that the atomic mass of Neon is equal to and its number in the periodic table is .
The mass of a proton is .
Hint
Solution
Energy conservation law gives :
Here, ( is the charge of an electron) and is equal to times the mass of a proton.
Thus :
.