Chapter 1

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 Right-hand 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 :

.

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Electrostatic energy of an electron
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magnetostatics